diff --git a/codes/classical/q-ary_digits/ag/rs/reed_solomon.yml b/codes/classical/q-ary_digits/ag/rs/reed_solomon.yml
index a10f2319d..e231ffd13 100644
--- a/codes/classical/q-ary_digits/ag/rs/reed_solomon.yml
+++ b/codes/classical/q-ary_digits/ag/rs/reed_solomon.yml
@@ -24,6 +24,7 @@ description: |
   An RS code with length \(n=q-1\) whose points \(\alpha_i\) are \(i-1\)st powers of a primitive \(n\)th root of unity is a \textit{narrow-sense RS code}.
   In an alternative convention (not used here), the primitive-root case is called an RS code, and the general-root case is a generalized RS code.
 
+
 protection: 'Since each polynomial \(f_{\mu}\) is of degree less than \(k\), it has less than \(k\) roots; this is called the \textit{degree mantra}.
 Therefore, the polynomial can be determined from its values at \(k\) points. This means that RS codes can correct erasures on up to \(n-k\) registers. The resulting distance, \(d=n-k+1\), saturates the Singleton bound.'
 
diff --git a/codes/quantum/groups/group_cluster_state.yml b/codes/quantum/groups/group_cluster_state.yml
new file mode 100644
index 000000000..5faf07419
--- /dev/null
+++ b/codes/quantum/groups/group_cluster_state.yml
@@ -0,0 +1,29 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: group_cluster_state
+physical: groups
+logical: groups
+
+name: 'Group-based cluster-state code'
+introduced: '\cite{arxiv:1408.6237}'
+
+description: |
+  Code consisting of (typically one) group-based cluster states based on a finite group \(G\) \cite{arxiv:1408.6237}.
+  Such cluster states can be defined using a graph and conditional group multiplication operations.
+
+
+relations:
+  parents:
+    - code_id: group_gkp
+      detail: 'Group-based cluster states are stabilized by \(X\)-type Pauli matrices representing \(G\) and generalized \(Z\)-type operators \cite{arxiv:1408.6237}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-04-03'
diff --git a/codes/quantum/groups/group_gkp.yml b/codes/quantum/groups/group_gkp.yml
index 940f3f225..f7aef5766 100644
--- a/codes/quantum/groups/group_gkp.yml
+++ b/codes/quantum/groups/group_gkp.yml
@@ -55,7 +55,8 @@ description: |
   \end{table}
 
 
-protection: 'Protects against generalized bit-flip errors \(g\in G\) that are inside the fundamental domain of \(G/K\). Protection against phase-flip errors determined by branching rules of irreps of \(G\) into those of \(K\), and further into those of \(H\).'
+protection: 'Protects against generalized bit-flip errors \(g\in G\) that are inside the fundamental domain of \(G/K\).
+Protection against phase-flip errors determined by branching rules of irreps of \(G\) into those of \(K\), and further into those of \(H\).'
 
 features:
   transversal_gates: 'Group-GKP codes corresponding to the \(G^{k_1} \subseteq G^{ k_2} \subset G^{n}\) group construction admit \(X\)-type transversal Pauli gates representing \(G\) \cite{arxiv:1902.07714}.'
@@ -76,8 +77,6 @@ relations:
       A single-mode qubit GKP code corresponds to the \(2\mathbb{Z}\subset\mathbb{Z}\subset\mathbb{R}\) group construction, and multimode GKP codes can be similarly described.
       An \([[n,k,d]]_{\mathbb{R}}\) analog stabilizer code corresponds to the \(\mathbb{R}^{ k_1} \subseteq \mathbb{R}^{ k_2} \subset \mathbb{R}^{n}\) group construction, where \(k=k_2/k_1\).
       GKP stabilizer codes for \(n\) modes correspond to subgroups \(\mathbb{Z}^m\) for \(m<n\).'
-    - code_id: cluster_state
-      detail: 'Cluster states can be generalized to finite groups \cite{arxiv:1408.6237}.'
 
 # Begin Entry Meta Information
 _meta:
diff --git a/codes/quantum/qubits/majorana/kitaev_chain.yml b/codes/quantum/qubits/majorana/kitaev_chain.yml
index f31ca09ff..baca1198f 100644
--- a/codes/quantum/qubits/majorana/kitaev_chain.yml
+++ b/codes/quantum/qubits/majorana/kitaev_chain.yml
@@ -11,7 +11,7 @@ name: 'Kitaev chain code'
 introduced: '\cite{arXiv:cond-mat/0010440}'
 
 description: |
-  An \([[n,1,1]]_{f}\) Majorana stabilizer code forming the ground-state of the Kitaev Majorana chain (a.k.a. Kitaev Majorana wire) in its fermionic topological phase, which is equivalent to the 1D quantum Ising model in the symmetry-breaking phase via the Jordan-Wigner transformation.
+  An \([[n,1,1]]_{f}\) Majorana stabilizer code forming the ground-state of the Kitaev Majorana chain (a.k.a. Kitaev Majorana wire) in its fermionic topological phase, which is unitarily equivalent to the 1D quantum Ising model in the symmetry-breaking phase via the Jordan-Wigner transformation.
   The code is usually defined using the algebra of two anti-commuting Majorana operators called \textit{Majorana zero modes (MZMs)} or \textit{Majorana edge modes (MEMs)}.
 
   Codewords have different values of the fermionic parity.
diff --git a/codes/quantum/qubits/nonstabilizer/cws/cws.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/cws.yml
similarity index 58%
rename from codes/quantum/qubits/nonstabilizer/cws/cws.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/cws.yml
index 495bd9821..9ca70a872 100644
--- a/codes/quantum/qubits/nonstabilizer/cws/cws.yml
+++ b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/cws.yml
@@ -12,22 +12,24 @@ short_name: 'CWS'
 introduced: '\cite{arXiv:cs/0610159,arXiv:0708.1021}'
 
 description: |
-  Member of a family of codes that strictly generalizes qubit stabilizer codes.
+  A code defined using a cluster state and a set of \(Z\)-type Pauli strings defined by a binary classical code.
 
-  They are usually denoted by \( \mathcal{Q} = (\mathcal{G},\mathcal{C}) \) where \(\mathcal{G}\) is a graph and \(\mathcal{C}\) is a \( (n,K,d) \) binary classical code.
-  From the graph we form the unique graph state (stabilizer state) \( |G \rangle \).
-  From the classical code we form Pauli \(Z\)-type operators \( W_i = Z^{c_{i,1}} \otimes \cdots \otimes Z^{c_{i,n}} \), where \(c_{i,j} \) is the \(j\)-th bit of the \(i\)-th classical codeword.
-  The CWS codewords are then \( | i \rangle =  W_i | G \rangle \).
+  The Galois-qudit CWS construction takes in \( \mathcal{Q} = (\mathcal{G},\mathcal{C}) \), where \(\mathcal{G}\) is a graph, and where \(\mathcal{C}\) is an \((n,K,d)\) binary code.
+  From the graph, we form the unique cluster state \( |\mathcal{G} \rangle \).
+  From the binary code, we form Pauli \(Z\)-type operators \( W_i = Z^{c_{i,1}} \otimes \cdots \otimes Z^{c_{i,n}} \), where \(c_{i,j} \) is the \(j\)-th coordinate of the \(i\)-th classical codeword.
+  The CWS codewords are then \( | i \rangle =  W_i | \mathcal{G} \rangle \).
 
-  The above definition corresponds to the \textit{standard form} of a CWS codes, and there is an alternative description that is locally Clifford-equivalent.
-  In particular, we can describe CWS codes as \( \mathcal{Q} = (S,\mathcal{W})\) where \(S\) is a stabilizer group and \( \mathcal{W} = \{ w_\ell \}_{\ell = 1}^K \) is a family of \(K\) \(n\)-qubit Pauli strings. We then form CWS codeswords as \( | i \rangle = w_i | S \rangle \), where \( | S \rangle \) is the (unique) stabilizer state of \(S\).
+  The above definition corresponds to the \textit{standard form} of CWS codes.
+  Since any stabilizer state is equivalent to a cluster state under a single-qubit Clifford circuit \cite{arxiv:quant-ph/0308151}\cite[Appx. A]{arxiv:1910.00471}, any code whose underlying state is a non-cluster stabilizer state is similarly equivalent to a CWS code.
 
   The term CWS was coined in Ref. \cite{arxiv:0708.1021}, and their approach is equivalent to another approach \cite{arXiv:cs/0610159} based on Boolean functions (see Ref. \cite{manual:{Zeng, Bei. Quantum operations and codes beyond the Stabilizer-Clifford framework. Diss. Massachusetts Institute of Technology, 2009.}}).
+  In an alternative convention (not used here), CWS codes are defined from an underlying stabilizer state that is not a necessarily a cluster state.
 
 
 protection: |
   Code distance \(\mathcal{Q} = ( \mathcal{G},\mathcal{C}) \) is upper bounded by the distance of the classical code \(\mathcal{C} \).
   The \hyperref[code:qubits_into_qubits]{diagonal distance} is upper bounded by \(\delta + 1\), where \(\delta\) is the minimum degree of \(\mathcal{G}\).
+
   Computing the distance is generally \(NP\)-complete, and is \(NP\)-hard for \hyperref[topic:degeneracy]{non-degenerate} codes \cite{arXiv:2203.04262}.
   Some bounds are provided in Ref. \cite{arxiv:1108.5490}.
 
@@ -46,15 +48,22 @@ notes:
 
 relations:
   parents:
-    - code_id: qsqc
-      detail: 'Restricting the underlying classical code to be symplectic self-dual reduces the \(((n,2^k L,d))\) QSQC construction to the \(((n,L,d))\) CWS construction \cite[Sec. IV.E]{arxiv:2311.07265}.'
+    - code_id: non_stabilizer
+      detail: 'Any CWS code can be written as a USt whose (\(K=1\)) stabilizer code is the cluster state and whose coset representatives are constructed from the binary classical code.
+      Conversely, USts are equivalent to CWS codes via a single-qubit Clifford circuit as follows \cite{arxiv:0907.2038,manual:{Li, Yunfan. Codeword Stabilized Quantum Codes and Their Error Correction. Diss. UC Riverside, 2010.}}\cite[Sec. 10.4]{doi:10.1017/CBO9781139034807.012}.
+      The set of coset representatives of any USt can be extended to a larger set iterating over the underlying stabilizer code such that all codewords can be obtained from a single stabilizer state.
+      Then, one can apply a single-qubit Clifford transformation to map said stabilizer state into a cluster state.'
     - code_id: qudit_cws
       detail: 'Modular-qudit CWS codes reduce to CWS codes for \(q=2\).'
     - code_id: galois_cws
       detail: 'Galois-qudit CWS codes reduce to CWS codes for \(q=2\).'
+    - code_id: qsqc
+      detail: 'Restricting the underlying classical code to be symplectic self-dual reduces the \(((n,2^k L,d))\) QSQC construction to the \(((n,L,d))\) CWS construction \cite[Sec. IV.E]{arxiv:2311.07265}.'
   cousins:
+    - code_id: cluster_state
+      detail: 'A single cluster-state codeword is used to construct a CWS code.'
     - code_id: movassagh_ouyang
-      detail: 'The Movassagh-Ouyang codes overlap the CWS codes but neither family is contained in the other.'
+      detail: 'The Movassagh-Ouyang codes overlap the CWS codes but neither family is contained in the other \cite{arXiv:2012.01453}.'
     - code_id: spacetime
       detail: 'CWS codes have been considered in the context of spacetime replication of quantum data \cite{arxiv:1210.0913,arXiv:1601.02544}, while STCs are designed to replicate classical data.'
 
@@ -63,6 +72,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2024-03-28'
     - user_id: VictorVAlbert
       date: '2022-04-21'
     - user_id: VictorVAlbert
diff --git a/codes/quantum/qubits/nonstabilizer/cws/qubit_10_24_3.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_10_24_3.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/cws/qubit_10_24_3.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_10_24_3.yml
diff --git a/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_5_6_2.yml
similarity index 88%
rename from codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_5_6_2.yml
index 5cbeed5f5..a3308e1ae 100644
--- a/codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml
+++ b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_5_6_2.yml
@@ -23,8 +23,6 @@ relations:
     - code_id: arvind
       detail: 'The \(((5,6,2))\) code is the \(((n,1+n(q-1),2))_q\) union stabilizer code for \(n=5\) and \(q=2\) \cite{arxiv:quant-ph/0210097}.'
     - code_id: quantum_cyclic
-    - code_id: non_stabilizer
-      detail: 'The six-qubit CWS code is a union stabilizer code \cite{arXiv:quant-ph/9703002,arxiv:quant-ph/0210097}.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qubits/nonstabilizer/cws/qubit_9_12_3.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_9_12_3.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/cws/qubit_9_12_3.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/qubit_9_12_3.yml
diff --git a/codes/quantum/qubits/nonstabilizer/cws/rains.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/rains.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/cws/rains.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/rains.yml
diff --git a/codes/quantum/qubits/nonstabilizer/cws/ssw.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/ssw.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/cws/ssw.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/cws/ssw.yml
diff --git a/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/non_stabilizer.yml
similarity index 68%
rename from codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/non_stabilizer.yml
index d8adefa09..380be3b82 100644
--- a/codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml
+++ b/codes/quantum/qubits/nonstabilizer/union_stabilizer/non_stabilizer.yml
@@ -7,7 +7,8 @@ code_id: non_stabilizer
 physical: qubits
 logical: qubits
 
-name: 'Union stabilizer code'
+name: 'Union stabilizer (USt) code'
+short_name: 'USt'
 introduced: '\cite{arXiv:quant-ph/9703002,arXiv:quant-ph/9703016,arxiv:quant-ph/9710031,arxiv:quant-ph/0210097,arxiv:0801.2144}'
 # First ref discusses unions of general codes
 
@@ -18,6 +19,13 @@ alternative_names:
 description: |
   A qubit code whose codespace consists of a direct sum of a qubit stabilizer codespace and one or more of that stabilizer code's error spaces.
 
+  Given a subset \(T\) of coset representatives of \(\mathsf{N}(\mathsf{S})/\mathsf{S}\) of a stabilizer code \([[n,k]]\) with codespace \(\mathsf{C}\) and stabilizer group \(\mathsf{S}\), one can construct the USt with codespace \cite[Def. 10.1]{doi:10.1017/CBO9781139034807.012}
+  \begin{align}
+    \mathsf{C}_{\text{USt}}=\bigoplus_{t\in T}t\mathsf{C}~.
+  \end{align}
+  The parameters of the USt are \(((n,2^k |T|))\), where \(|T|\) is the number of chosen coset representatives.
+  A USt is \textit{CSS-like} when the underlying stabilizer code is CSS, so the coset representatives from the two classical codes underlying the CSS code.
+
   Union stabilizer codes constructed in Ref. \cite{arxiv:quant-ph/0210097} include the \(((33, 155, 3))\) and \(((15, 8, 3))\) codes.
 
 
@@ -31,8 +39,9 @@ notes:
 
 relations:
   parents:
-    - code_id: cws
-      detail: 'Union stabilizer codes can be defined as CWS codes \cite{arxiv:0907.2038,manual:{Li, Yunfan. Codeword Stabilized Quantum Codes and Their Error Correction. Diss. UC Riverside, 2010.}}\cite[Sec. 10.4]{doi:10.1017/CBO9781139034807.012}.'
+    - code_id: qubits_into_qubits
+    - code_id: qudit_non_stabilizer
+      detail: 'Modular-qudit union stabilizer codes reduce to union stabilizer codes for \(q=2\).'
     - code_id: galois_non_stabilizer
       detail: 'Galois-qudit union stabilizer codes reduce to union stabilizer codes for \(q=2\).'
   cousins:
diff --git a/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml b/codes/quantum/qubits/nonstabilizer/union_stabilizer/quantum_goethals_preparata.yml
similarity index 94%
rename from codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml
rename to codes/quantum/qubits/nonstabilizer/union_stabilizer/quantum_goethals_preparata.yml
index 4796d0043..754aba594 100644
--- a/codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml
+++ b/codes/quantum/qubits/nonstabilizer/union_stabilizer/quantum_goethals_preparata.yml
@@ -11,7 +11,7 @@ name: '\(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code'
 introduced: '\cite{arXiv:0801.2144,arxiv:0801.2150}'
 
 description: |
-  Member of a family of \(((2^m,2^{2^m−5m+1},8))\) CWS codes constructed using the classical Goethals and Preparata codes.
+  Member of a family of \(((2^m,2^{2^m−5m+1},8))\) CSS-like union stabilizer codes constructed using the classical Goethals and Preparata codes.
 
   They can be viewed as union stabilizer codes constructed from the codespace of a \([[2^m,2^m-7m+3,8]]\) code (which itself is obtained from the Steane enlargement construction) and the coset representatives used to obtain the Goethals and Preparata codes \cite[Thm. 10.3]{doi:10.1017/CBO9781139034807.012}.
 
diff --git a/codes/quantum/qubits/nonstabilizer/xp_stabilizer.yml b/codes/quantum/qubits/nonstabilizer/xp_stabilizer/xp_stabilizer.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/xp_stabilizer.yml
rename to codes/quantum/qubits/nonstabilizer/xp_stabilizer/xp_stabilizer.yml
diff --git a/codes/quantum/qubits/nonstabilizer/xs_stabilizer.yml b/codes/quantum/qubits/nonstabilizer/xp_stabilizer/xs_stabilizer.yml
similarity index 100%
rename from codes/quantum/qubits/nonstabilizer/xs_stabilizer.yml
rename to codes/quantum/qubits/nonstabilizer/xp_stabilizer/xs_stabilizer.yml
diff --git a/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml b/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml
index 84eb9a9b4..7123da17b 100644
--- a/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml
+++ b/codes/quantum/qubits/small_distance/small/stab_5_1_3.yml
@@ -93,7 +93,7 @@ relations:
     - code_id: majorana_stab
       detail: 'The five-qubit code Hamiltonian is local when expressed in terms of mutually commuting Majorana operators \cite{manual:{Aleksander Kubica, private communication, 2019}}.'
     - code_id: qubits_into_qubits
-      detail: 'Every \(((5,2,3))\) code is equivalent to the five-qubit code \cite[Corr. 10]{arxiv:quant-ph/9704043}.'
+      detail: 'Every \(((5,2,3))\) code is single-qubit-Clifford-equivalent to the five-qubit code \cite[Corr. 10]{arxiv:quant-ph/9704043}.'
     - code_id: quantum_concatenated
       detail: 'The concatenated five-qubit code has a \hyperref[topic:measurement-threshold]{measurement threshold} of one \cite{arxiv:2402.00145}.'
     - code_id: cws
diff --git a/codes/quantum/qubits/small_distance/small/steane/steane.yml b/codes/quantum/qubits/small_distance/small/steane/steane.yml
index 100d40d66..e874a3c6c 100644
--- a/codes/quantum/qubits/small_distance/small/steane/steane.yml
+++ b/codes/quantum/qubits/small_distance/small/steane/steane.yml
@@ -93,8 +93,9 @@ relations:
       detail: 'The Steane code is a group-representation code with \(G\) being the \(2O\) subgroup of \(SU(2)\) \cite{arxiv:2306.11621}.'
     - code_id: concatenated_steane
       detail: 'The concatenated Steane code at level \(m=1\) is the Steane code.'
+  cousins:
     - code_id: quantum_cyclic
-      detail: 'The Steade code is equivalent to a cyclic code via qubit permutations \cite[Exam. 1]{arxiv:1108.5490}.'
+      detail: 'The Steane code is equivalent to a cyclic code via qubit permutations \cite[Exam. 1]{arxiv:1108.5490}.'
 
 
 #      detail: 'Steane code is the smallest member of a family of Reed-Muller-based CSS codes.'
diff --git a/codes/quantum/qubits/stabilizer/fermion_into_qubit/bksf.yml b/codes/quantum/qubits/stabilizer/fermion_into_qubit/bksf.yml
index 518a7b909..cc86bdd8c 100644
--- a/codes/quantum/qubits/stabilizer/fermion_into_qubit/bksf.yml
+++ b/codes/quantum/qubits/stabilizer/fermion_into_qubit/bksf.yml
@@ -29,7 +29,7 @@ relations:
     - code_id: mlsc
       detail: 'The BKSF code can be thought of as a particular MLSC \cite{arxiv:1812.08190}.'
     - code_id: 2d_bosonization
-      detail: 'The BKSF code is equivalent to a distance-two 2D bosonization code for a specific edge ordering \cite{arxiv:2201.05153}.'
+      detail: 'The BKSF code is a distance-two 2D bosonization code for a specific edge ordering \cite{arxiv:2201.05153}.'
 # cousins:
 #   - code_id: triangular_color
 #     detail: 'The square-lattice BKSF encoding \cite{arxiv:1810.05274} has the excitation structure as one of the toric codes underlying the 2D color code \cite{manual:{Compact fermion to qubit mappings for quantum simulation}}.'
diff --git a/codes/quantum/qubits/stabilizer/fracton/checkerboard.yml b/codes/quantum/qubits/stabilizer/fracton/checkerboard.yml
index aaec85481..da7d8a721 100644
--- a/codes/quantum/qubits/stabilizer/fracton/checkerboard.yml
+++ b/codes/quantum/qubits/stabilizer/fracton/checkerboard.yml
@@ -12,7 +12,7 @@ introduced: '\cite{arXiv:1505.02576}'
 
 description: |
   A foliated type-I fracton code defined on a cubic lattice that admits weight-eight  \(X\)- and \(Z\)-type stabilizer generators on the eight vertices of each cube in the lattice.
-  
+
   Variants include the twisted checkerboard model \cite{arxiv:1805.06899}.
 
 features:
@@ -26,10 +26,10 @@ relations:
   parents:
     - code_id: qubit_css
     - code_id: fracton
-      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local unitary \cite{arxiv:1806.08633}. Hence, it is a foliated type-I fracton code.'
+      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local constant-depth unitary \cite{arxiv:1806.08633}. Hence, it is a foliated type-I fracton code.'
   cousins:
     - code_id: xcube
-      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local unitary \cite{arxiv:1806.08633}.'
+      detail: 'The checkerboard model is equivalent to two copies of the X-cube model via a local constant-depth unitary \cite{arxiv:1806.08633}.'
 
 
 _meta:
diff --git a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml
index 171956332..8986982af 100644
--- a/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml
+++ b/codes/quantum/qubits/stabilizer/mbqc/cluster_state.yml
@@ -14,17 +14,19 @@ alternative_names:
   - 'Graph-state code'
 
 description: |
-  Code consisting of cluster states \cite{arxiv:quant-ph/0004051}, which are stabilizer states defined on a graph. There is one stabilizer generator \(S_v\) per graph vertex \(v\) of the form
+  Code consisting of (typically one) cluster states \cite{arxiv:quant-ph/0004051}.
+  Often used in measurement-based quantum computation (MBQC), which substitutes the temporal dimension necessary for decoding a conventional code with a spatial dimension.
+  This is done by encoding the computation into the features of the cluster state''s graph.
+
+  Cluster states are stabilizer states defined on a graph.
+  There is one stabilizer generator \(S_v\) per graph vertex \(v\) of the form
   \begin{align}
     S_v = X_{v} \prod_{w\in N(v)} Z_w~,
   \end{align}
   where the neighborhood \(N(v)\) is the set of vertices which share an edge with \(v\).
 
-  Cluster-state codewords are used in measurement-based quantum computation (MBQC), which substitutes the temporal dimension necessary for decoding with a spatial dimension.
-  This is done by encoding the computation into the topological features of the cluster state''s graph.
-
   An MBQC scheme can be constructed out of any qubit CSS code (via \textit{foliation} \cite{arxiv:1607.02579}) or qubit stabilizer code \cite{arxiv:1811.11780}.
-  The original MBQC scheme \cite{arxiv:quant-ph/0510135,arxiv:quant-ph/0610082} uses the RBH cluster state on the bcc lattice (equivalently, a cubic lattice with qubits on edges and faces).
+  The original MBQC scheme \cite{arxiv:quant-ph/0510135,arxiv:quant-ph/0610082} uses the RBH cluster state on the bcc lattice (i.e., a cubic lattice with qubits on edges and faces).
 
 protection: |
   Protection is related to the stabilizer code underlying the cluster state.
@@ -84,9 +86,11 @@ relations:
   parents:
     - code_id: qubit_stabilizer
       detail: 'Cluster states are particular qubit stabilizer states defined on a graph.
-      Any qubit stabilizer code is locally equivalent to a graph code \cite{arxiv:quant-ph/0111080} (see also \cite{arxiv:quant-ph/0703112}).
-      As a corollary, any qubit stabilizer state is locally equivalent to a cluster state \cite{arxiv:quant-ph/0308151}\cite[Appx. A]{arxiv:1910.00471}.
+      Any qubit stabilizer code is equivalent to a graph code via a single-qubit Clifford circuit \cite{arxiv:quant-ph/0111080} (see also \cite{arxiv:quant-ph/0703112}).
+      As a corollary, any qubit stabilizer state is equivalent to a cluster state under a single-qubit Clifford circuit \cite{arxiv:quant-ph/0308151}\cite[Appx. A]{arxiv:1910.00471}.
       Any fault-tolerant scheme based on qubit stabilizer codes can be mapped into a cluster-state based MBQC protocol \cite{arxiv:1811.11780}.'
+    - code_id: group_cluster_state
+      detail: 'Group-based cluster-state codes reduce to cluster-state codes for \(G=\mathbb{Z}_2\).'
   cousins:
     - code_id: fusion
       detail: 'FBQC and MBQC are both computational models in which computation is done by measuring resource states (which are qubit stabilizer states).
diff --git a/codes/quantum/qubits/stabilizer/mbqc/rbh.yml b/codes/quantum/qubits/stabilizer/mbqc/rbh.yml
index 37f867004..e0857de97 100644
--- a/codes/quantum/qubits/stabilizer/mbqc/rbh.yml
+++ b/codes/quantum/qubits/stabilizer/mbqc/rbh.yml
@@ -13,7 +13,7 @@ introduced: '\cite{arxiv:quant-ph/0407255,arxiv:quant-ph/0510135,arxiv:quant-ph/
 
 description: |
   Also called an \textit{RHG (Raussendorf-Harrington-Goyal) cluster-state code}.
-  A three-dimensional cluster-state code defined on the bcc lattice (equivalently, a cubic lattice with qubits on edges and faces).
+  A three-dimensional cluster-state code defined on the bcc lattice (i.e., a cubic lattice with qubits on edges and faces).
 
   The MBQC version of the code is defined as the unique ground state of a certain code Hamiltonian. This state is the resource state used in the first MBQC scheme \cite{arxiv:quant-ph/0510135,arxiv:quant-ph/0610082}.
   It encodes the temporal gate operations on the surface code into a third spatial dimension.
diff --git a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml
index ee019ad37..d878784a4 100644
--- a/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml
+++ b/codes/quantum/qubits/stabilizer/qubit_stabilizer.yml
@@ -10,8 +10,13 @@ logical: qubits
 name: 'Qubit stabilizer code'
 introduced: '\cite{arXiv:quant-ph/9605005,arXiv:quant-ph/9705052}'
 
+alternative_names:
+  - 'Pauli stabilizer code'
+  - 'Additive quantum code'
+  - 'Additive CWS code'
+
 description: |
-  Also called a \textit{Pauli stabilizer code}. An \(((n,2^k,d))\) qubit stabilizer code is denoted as \([[n,k]]\) or \([[n,k,d]]\), where \(d\) is the code's distance. Logical subspace is the joint eigenspace of commuting Pauli operators forming the code's stabilizer group \(\mathsf{S}\). Traditionally, the logical subspace is the joint \(+1\) eigenspace of a set of \(2^{n-k}\) commuting Pauli operators which do not contain \(-I\). The distance is the minimum weight of a Pauli string that implements a nontrivial logical operation in the code.
+  An \(((n,2^k,d))\) qubit stabilizer code is denoted as \([[n,k]]\) or \([[n,k,d]]\), where \(d\) is the code's distance. Logical subspace is the joint eigenspace of commuting Pauli operators forming the code's stabilizer group \(\mathsf{S}\). Traditionally, the logical subspace is the joint \(+1\) eigenspace of a set of \(2^{n-k}\) commuting Pauli operators which do not contain \(-I\). The distance is the minimum weight of a Pauli string that implements a nontrivial logical operation in the code.
 
   \begin{defterm}{Binary symplectic representation}
   \label{topic:binary-symplectic-representation}
@@ -130,7 +135,8 @@ notes:
 relations:
   parents:
     - code_id: non_stabilizer
-      detail: 'A union stabilizer code reduces to a stabilizer code when there are no error spaces included in the code.'
+      detail: 'A stabilizer code with stabilizer group \(\mathsf{S}\) can be thought of as a USt with no coset representatives.
+      Conversely, if the set of coset representatives of a USt form a linear binary code, then they can be absorbed into a stabilizer group that defines the USt.'
     - code_id: xp_stabilizer
       detail: 'The XP stabilizer formalism reduces to the Pauli formalism at \(N=2\).'
     - code_id: qudit_stabilizer
@@ -144,6 +150,8 @@ relations:
       detail: 'Galois-qudit stabilizer codes for \(q=2\) correspond to qubit stabilizer codes.'
     - code_id: qubit_stabilizer_oaqecc
   cousins:
+    - code_id: cws
+      detail: 'CWS codes whose underlying classical code is a linear binary code are qubit stabilizer codes containing a cluster-state codeword.'
     - code_id: binary_linear
       detail: 'Qubit stabilizer codes are the closest quantum analogues of binary linear codes because addition modulo two corresponds to multiplication of stabilizers in the quantum case.
       Any binary linear code can be thought of as a qubit stabilizer code with \(Z\)-type stabilizer generators \cite[Table I]{arxiv:quant-ph/0610088}.
diff --git a/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml b/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
index b48e7cb83..d466b8ceb 100644
--- a/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
+++ b/codes/quantum/qubits/stabilizer/rm/quantum_hamming_css.yml
@@ -29,7 +29,7 @@ features:
 relations:
   parents:
     - code_id: quantum_reed_muller
-      detail: '\([[2^r-1, 2^r-2r-1, 3]]\) quantum Hamming codes are quantum Reed-Muller codes because they are formed from classical Hamming codes, which are equivalent to RM\((r-2,r)\).'
+      detail: '\([[2^r-1, 2^r-2r-1, 3]]\) quantum Hamming codes are quantum Reed-Muller codes because they are formed from classical Hamming codes RM\((r-2,r)\).'
     - code_id: qudit_hamming_css
       detail: '\([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code for \(p=2\) reduce to \([[2^r-1, 2^r-2r-1, 3]]\) quantum Hamming codes.'
   cousins:
diff --git a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml
index d69a377a4..789c0a71d 100644
--- a/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml
+++ b/codes/quantum/qubits/stabilizer/topological/color/2d_color/2d_color.yml
@@ -73,10 +73,10 @@ relations:
     - code_id: galois_topological
       detail: 'Galois-qudit 2D color codes reduce to 2D color codes for \(q=2\).'
     - code_id: quantum_double_abelian
-      detail: 'When treated as ground states of the code Hamiltonian, states of the color code on a torus geometry realize \(\mathbb{Z}_2\times\mathbb{Z}_2\) topological order \cite{arxiv:0906.4127}, equivalent to the phase realized by two copies of the surface code \cite{arxiv:1503.02065}.'
+      detail: 'When treated as ground states of the code Hamiltonian, states of the color code on a torus geometry realize \(\mathbb{Z}_2\times\mathbb{Z}_2\) topological order \cite{arxiv:0906.4127}, equivalent to the phase realized by two copies of the surface code via a local constant-depth Clifford circuit \cite{arxiv:1503.02065}.'
   cousins:
     - code_id: surface
-      detail: 'The 2D color code is equivalent to multiple decoupled copies of the 2D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.
+      detail: 'The 2D color code is equivalent to multiple decoupled copies of the 2D surface code via a local constant-depth Clifford circuit \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.
       Conversely, the 2D color code can \hyperref[topic:code-switching]{condense} to form the 2D surface code in nine different ways, i.e., by adding two body hopping terms along one of its three triangular directions to the stabilizer group and then taking the center of the resulting nonabelian group \cite{arxiv:2212.00042}.
       Both the surface and 2D color codes can be constructed from two distinct types of lattices, namely, 4-valent and 3-valent 3-colorable lattices, respectively \cite{arxiv:1107.3502}.'
     - code_id: 3d_color
diff --git a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
index 028f526c3..bc847379c 100644
--- a/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
+++ b/codes/quantum/qubits/stabilizer/topological/color/3d_color.yml
@@ -39,7 +39,7 @@ relations:
     - code_id: quantum_triorthogonal
   cousins:
     - code_id: 3d_surface
-      detail: 'The 3D color code is equivalent to multiple decoupled copies of the 3D surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.'
+      detail: 'The 3D color code is equivalent to multiple decoupled copies of the 3D surface code via a local constant-depth Clifford circuit \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.'
     - code_id: xs_stabilizer
       detail: 'The 3D color code admits XS stabilizers; see \href{https://www.youtube.com/watch?v=B8h5-ANc_-8}{talk by M. Kesselring at the 2020 FTQC conference} and the related \cite[Exam. 6.4]{arxiv:2203.00103}.'
 
diff --git a/codes/quantum/qubits/stabilizer/topological/color/color.yml b/codes/quantum/qubits/stabilizer/topological/color/color.yml
index 4033bb577..00595cdf1 100644
--- a/codes/quantum/qubits/stabilizer/topological/color/color.yml
+++ b/codes/quantum/qubits/stabilizer/topological/color/color.yml
@@ -41,7 +41,7 @@ relations:
       detail: 'Color codes are special cases of quantum pin codes \cite[Sec. II.E]{arxiv:1906.11394}'
   cousins:
     - code_id: higher_dimensional_surface
-      detail: 'The color code on a \(D\)-dimensional closed manifold is equivalent to multiple decoupled copies of the \(D\)-dimensional surface code \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.
+      detail: 'The color code on a \(D\)-dimensional closed manifold is equivalent to multiple decoupled copies of the \(D\)-dimensional surface code via a local constant-depth Clifford circuit \cite{arxiv:1007.4601,arxiv:1503.02065,arXiv:1804.00866}.
       Several hybrid color-surface codes exist \cite{arxiv:2112.01446,arxiv:2201.12450}.'
 
 
diff --git a/codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml b/codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml
index 551e97c4d..021695667 100644
--- a/codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml
+++ b/codes/quantum/qubits/subsystem/topological/subsystem_three_fermion.yml
@@ -14,7 +14,7 @@ introduced: '\cite{arxiv:0811.0911,arXiv:2211.03798}'
 description: |
   2D subsystem stabilizer code whose low-energy excitations realize the three-fermion anyon theory \cite{arxiv:0712.1377,arxiv:0811.0911,arxiv:1103.4606}.
   One version uses two qubits at each site \cite{arXiv:2211.03798}, while other manifestations utilize a single qubit per site and only two-body interactions \cite{arxiv:0811.0911,arxiv:0908.4246}.
-  All are expected to be equivalent to each other under local Clifford transformations.
+  All are expected to be equivalent to each other via a local constant-depth Clifford circuit.
 
 
 relations:
diff --git a/codes/quantum/qudits/small/qudit_3_6_2.yml b/codes/quantum/qudits/nonstabilizer/qudit_3_6_2.yml
similarity index 90%
rename from codes/quantum/qudits/small/qudit_3_6_2.yml
rename to codes/quantum/qudits/nonstabilizer/qudit_3_6_2.yml
index 368d45873..854f07bc1 100644
--- a/codes/quantum/qudits/small/qudit_3_6_2.yml
+++ b/codes/quantum/qudits/nonstabilizer/qudit_3_6_2.yml
@@ -9,10 +9,11 @@ logical: qudits
 
 name: '\(((3,6,2))_{\mathbb{Z}_6}\) code'
 introduced: '\cite{arXiv:2104.05122}'
+# Qudits labeled by Z_6
 
 description: |
   Six-qudit error-detecting code with logical dimension \(K=6\) that is obtained from a particular maximally entangled state that serves as a solution to the 36 officers of Euler problem.
-
+  The code is obtained from a \(((4,1,3))_{\mathbb{Z}_6}\) code.
 
 relations:
   parents:
diff --git a/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_cws.yml b/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_cws.yml
new file mode 100644
index 000000000..24864e0a3
--- /dev/null
+++ b/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_cws.yml
@@ -0,0 +1,44 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: qudit_cws
+physical: qudits
+logical: qudits
+
+name: 'Modular-qudit CWS code'
+introduced: '\cite{arXiv:0712.1979,arXiv:0801.0831}'
+
+description: |
+  A CWS code for modular qudits, defined using a modular-qudit cluster state and a set of modular-qudit \(Z\)-type Pauli strings defined by a \(q\)-ary classical code over \(\mathbb{Z}_q\).
+
+  The modular-qudit CWS construction takes in \( \mathcal{Q} = (\mathcal{G},\mathcal{C}) \), where \(\mathcal{G}\) is a graph, and where \(\mathcal{C}\) is an \((n,K,d)_{\mathbb{Z}_q}\) \(q\)-ary code over \(\mathbb{Z}_q\).
+  From the graph, we form the modular-qudit cluster state \( |\mathcal{G} \rangle \).
+  From the \(q\)-ary code, we form modular-qudit Pauli \(Z\)-type operators \( W_i = Z^{c_{i,1}} \otimes \cdots \otimes Z^{c_{i,n}} \), where \(c_{i,j} \) is the \(j\)-th coordinate of the \(i\)-th classical codeword.
+  The codewords are then \( | i \rangle =  W_i | \mathcal{G} \rangle \).
+
+  In an alternative convention (not used here), CWS codes are defined from an underlying modular-qudit stabilizer state that is not a necessarily a cluster state.
+
+notes:
+  - 'See Ref. \cite{arxiv:0712.1979} for qudit CWS code tables.'
+
+relations:
+  parents:
+    - code_id: qudit_non_stabilizer
+      detail: 'Any modular-qudit CWS code can be written as a modular-qudit USt whose (\(K=1\)) stabilizer code is the cluster state and whose coset representatives are constructed from the \(q\)-ary classical code over \(\mathbb{Z}_q\).
+      Conversely, modular-qudit USts are equivalent to modular-qudit CWS codes via a single-Galois-qudit Clifford circuit as follows \cite{arxiv:0907.2038,manual:{Li, Yunfan. Codeword Stabilized Quantum Codes and Their Error Correction. Diss. UC Riverside, 2010.}}\cite[Sec. 10.4]{doi:10.1017/CBO9781139034807.012}.
+      The set of coset representatives of any modular-qudit USt can be extended to a larger set iterating over the underlying stabilizer code such that all codewords can be obtained from a single stabilizer state.
+      Then, one can apply a single-qubit Clifford transformation to map said stabilizer state into a cluster state.'
+    - code_id: group_cluster_state
+      detail: 'A single group-based cluster-state codeword for \(G=\mathbb{Z}_q\) is used to construct a modular-qudit CWS code.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-03-28'
+    - user_id: VictorVAlbert
+      date: '2024-02-11'
diff --git a/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_non_stabilizer.yml b/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_non_stabilizer.yml
new file mode 100644
index 000000000..b1f3cecbb
--- /dev/null
+++ b/codes/quantum/qudits/nonstabilizer/union_stabilizer/qudit_non_stabilizer.yml
@@ -0,0 +1,35 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: qudit_non_stabilizer
+physical: qudits
+logical: qudits
+
+name: 'Modular-qudit USt code'
+introduced: '\cite{arXiv:0712.1979,arXiv:0801.0831}'
+
+description: |
+  A modular-qubit code whose codespace consists of a direct sum of a modular-qubit stabilizer codespace and one or more of that stabilizer code's error spaces.
+
+  Given a subset \(T\) of coset representatives of \(\mathsf{N}(\mathsf{S})/\mathsf{S}\) of a modular-qudit stabilizer code \(((n,K))\) with codespace \(\mathsf{C}\) and stabilizer group \(\mathsf{S}\), one can construct the modular-qudit USt with codespace
+  \begin{align}
+    \mathsf{C}_{\text{USt}}=\bigoplus_{t\in T}t\mathsf{C}~.
+  \end{align}
+  The parameters of the USt are \(((n,K|T|,d))\), where \(|T|\) is the number of chosen coset representatives.
+  A modular-qudit USt is \textit{CSS-like} when the underlying stabilizer code is CSS, so the coset representatives from the two classical codes underlying the CSS code.
+
+relations:
+  parents:
+    - code_id: qudits_into_qudits
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-03-28'
+    - user_id: VictorVAlbert
+      date: '2024-02-11'
diff --git a/codes/quantum/qudits/qudit_cws.yml b/codes/quantum/qudits/qudit_cws.yml
deleted file mode 100644
index e14c0b45b..000000000
--- a/codes/quantum/qudits/qudit_cws.yml
+++ /dev/null
@@ -1,29 +0,0 @@
-#######################################################
-## This is a code entry in the error correction zoo. ##
-##       https://github.com/errorcorrectionzoo       ##
-#######################################################
-
-code_id: qudit_cws
-physical: qudits
-logical: qudits
-
-name: 'Modular-qudit CWS code'
-introduced: '\cite{arXiv:0712.1979,arXiv:0801.0831}'
-
-description: |
-  A CWS code for modular qudits.
-
-notes:
-  - 'See Ref. \cite{arxiv:0712.1979} for qudit CWS code tables.'
-
-relations:
-  parents:
-    - code_id: qudits_into_qudits
-
-
-# Begin Entry Meta Information
-_meta:
-  # Change log - most recent first
-  changelog:
-    - user_id: VictorVAlbert
-      date: '2024-02-11'
diff --git a/codes/quantum/qudits/stabilizer/3d_stabilizer.yml b/codes/quantum/qudits/stabilizer/3d_stabilizer.yml
index 310a71e0e..bdeab59ca 100644
--- a/codes/quantum/qudits/stabilizer/3d_stabilizer.yml
+++ b/codes/quantum/qudits/stabilizer/3d_stabilizer.yml
@@ -12,7 +12,7 @@ name: '3D lattice stabilizer code'
 
 description: |
   Lattice stabilizer code in three spatial dimensions.
-  Qubit codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code \cite{arXiv:1908.08049}.
+  Qubit codes are conjectured to admit either fracton phases or abelian topological phases that are equivalent to multiple copies of the 3D surface code and/or the 3D fermionic surface code via a local constant-depth Clifford circuit \cite{arXiv:1908.08049}.
 
 # 1. \textit{Abelian topological phase}: Excitations are mobile in all 3 dimensions, as is typical in a topological code. Such codes are conjectured to be equivalent to a \(\mathbb{Z}_2\) gauge theory, i.e., multiple copies of the 3D surface code or the 3D fermionic surface code.
 
diff --git a/codes/quantum/qudits/frobenius.yml b/codes/quantum/qudits/stabilizer/frobenius.yml
similarity index 100%
rename from codes/quantum/qudits/frobenius.yml
rename to codes/quantum/qudits/stabilizer/frobenius.yml
diff --git a/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml b/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml
index 923e6f23b..f6135de39 100644
--- a/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml
+++ b/codes/quantum/qudits/stabilizer/qudit_stabilizer.yml
@@ -11,9 +11,14 @@ name: 'Modular-qudit stabilizer code'
 introduced: '\cite{arXiv:quant-ph/9705052}'
 
 description: |
-  An \(((n,K,d))_q\) modular-qudit code whose logical subspace is the joint eigenspace of commuting qudit Pauli operators forming the code's stabilizer group \(\mathsf{S}\). Traditionally, the logical subspace is the joint \(+1\) eigenspace, and the stabilizer group does not contain \(e^{i \phi} I\) for any \(\phi \neq 0\). The distance \(d\) is the minimum weight of a qudit Pauli string that implements a nontrivial logical operation in the code.
+  An \(((n,K,d))_q\) modular-qudit code whose logical subspace is the joint eigenspace of commuting qudit Pauli operators forming the code's stabilizer group \(\mathsf{S}\).
+  Traditionally, the logical subspace is the joint \(+1\) eigenspace, and the stabilizer group does not contain \(e^{i \phi} I\) for any \(\phi \neq 0\).
+  The distance \(d\) is the minimum weight of a qudit Pauli string that implements a nontrivial logical operation in the code.
 
-  A modular-qudit stabilizer code encoding an integer number of qudits (\(K=q^k\)) is denoted as \([[n,k]]_{\mathbb{Z}_q}\) or \([[n,k,d]]_{\mathbb{Z}_q}\). For composite \(q\), such codes need not encode an integer number of qudits, with \(K=q^n/|\mathsf{S}|\) \cite{arxiv:1101.1519}. This is because \(|{\mathsf{S}}|\) need not be a power of \(q\), as group generators may have different orders. As a result, \([[n,k,d]]\) notation is often used with non-integer \(k=\log_q K\). \textit{Prime-qudit} stabilizer codes, where \(q=p\) for some prime \(p\), do not suffer from this issue and encode \(n-k\) logical qudits, with \(K=p^{n-k}\).
+  A modular-qudit stabilizer code encoding an integer number of qudits (\(K=q^k\)) is denoted as \([[n,k]]_{\mathbb{Z}_q}\) or \([[n,k,d]]_{\mathbb{Z}_q}\).
+  For composite \(q\), such codes need not encode an integer number of qudits, with \(K=q^n/|\mathsf{S}|\) \cite{arxiv:1101.1519}.
+  This is because \(|{\mathsf{S}}|\) need not be a power of \(q\), as group generators may have different orders. As a result, \([[n,k,d]]\) notation is often used with non-integer \(k=\log_q K\).
+  \textit{Prime-qudit} stabilizer codes, where \(q=p\) for some prime \(p\), do not suffer from this issue and encode \(n-k\) logical qudits, with \(K=p^{n-k}\).
 
   Each code can be represented by a \textit{check matrix} (a.k.a. \textit{stabilizer generator matrix}) \(H=(A|B)\), where each row \((a|b)\) is the \(q\)-ary symplectic representation of a stabilizer generator. The check matrix can be brought into standard form via Gaussian elimination \cite{arxiv:1101.1519}.
 
@@ -51,12 +56,15 @@ notes:
 
 relations:
   parents:
-    - code_id: qudit_cws
-      detail: 'Modular-qudit CWS codes are a generalization of modular-qudit stabilizer codes \cite[Corr. 4-5]{arxiv:1505.00283}.'
+    - code_id: qudit_non_stabilizer
+      detail: 'A modular-qudit stabilizer code with stabilizer group \(\mathsf{S}\) can be thought of as a modular-qudit USt with no coset representatives.
+      Conversely, if \(K = q^k\), and if the set of coset representatives of a modular-qudit USt form a \(q\)-ary linear code over \(\mathbb{Z}_q\), then they can be absorbed into a modular-qudit stabilizer group that defines the USt.'
     - code_id: stabilizer
     - code_id: quantum_lego
       detail: 'Modular-qudit stabilizer codes are quantum Lego codes built out of atomic blocks such as the 2-qudit repetition code, single-qudit trivial stabilizer codes, and tensor-products of the \(|0\rangle\) state.'
   cousins:
+    - code_id: qudit_cws
+      detail: 'Modular-qudit CWS codes whose underlying classical code is a linear \(q\)-ary code over \(\mathbb{Z}_q\) are modular-qudit stabilizer codes containing a cluster-state codeword; see \cite[Corr. 4-5]{arxiv:1505.00283}, which defines CWS codes as admitting an underlying stabilizer state that is not a necessarily a cluster state.'
     - code_id: q-ary_over_zq
       detail: 'Modular-qudit stabilizer codes are the closest quantum analogues of additive codes over \(\mathbb{Z}_q\) because addition in the ring corresponds to multiplication of stabilizers in the quantum case.'
 
diff --git a/codes/quantum/qudits_galois/nonstabilizer/galois_cws.yml b/codes/quantum/qudits_galois/nonstabilizer/galois_cws.yml
index 14dce0139..5dd60e239 100644
--- a/codes/quantum/qudits_galois/nonstabilizer/galois_cws.yml
+++ b/codes/quantum/qudits_galois/nonstabilizer/galois_cws.yml
@@ -11,12 +11,21 @@ name: 'Galois-qudit CWS code'
 # introduced: '\cite{arXiv:0712.1979,arXiv:0801.0831}'
 
 description: |
-  A CWS code for Galois qudits.
-  This entry has not yet been developed in the literature.
+  A CWS code for Galois qudits, defined using a Galois-qudit cluster state and a set of Galois-qudit \(Z\)-type Pauli strings defined by a \(q\)-ary classical code.
+
+  This entry has not yet been developed in the literature, so the formulation below is a conjecture.
+  The Galois-qudit CWS construction takes in \( \mathcal{Q} = (\mathcal{G},\mathcal{C}) \), where \(\mathcal{G}\) is a graph, and where \(\mathcal{C}\) is an \((n,K,d)_q\) \(q\)-ary code.
+  From the graph, we form the Galois-qudit cluster state \( |\mathcal{G} \rangle \).
+  From the \(q\)-ary code, we form Galois-qudit Pauli \(Z\)-type operators \( W_i = Z^{c_{i,1}} \otimes \cdots \otimes Z^{c_{i,n}} \), where \(c_{i,j} \) is the \(j\)-th coordinate of the \(i\)-th classical codeword.
+  The codewords are then \( | i \rangle =  W_i | \mathcal{G} \rangle \).
 
 relations:
   parents:
-    - code_id: galois_into_galois
+    - code_id: galois_non_stabilizer
+      detail: 'Any Galois-qudit CWS code can be written as a USt whose (\(K=1\)) stabilizer code is the cluster state and whose coset representatives are constructed from the \(q\)-ary classical code.'
+  cousins:
+    - code_id: group_cluster_state
+      detail: 'A group-based cluster-state codeword for \(G=GF(q)\) is used to construct a modular-qudit CWS code.'
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml b/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml
index cf30cbd4e..fcf6f5061 100644
--- a/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml
+++ b/codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml
@@ -7,7 +7,7 @@ code_id: galois_non_stabilizer
 physical: galois
 logical: galois
 
-name: 'Galois-qudit union stabilizer code'
+name: 'Galois-qudit USt code'
 introduced: '\cite{arXiv:quant-ph/9703002,arXiv:quant-ph/9703016,arxiv:quant-ph/9710031,arxiv:quant-ph/0210097,arxiv:0801.2144}'
 # First ref discusses unions of general codes
 
@@ -16,15 +16,22 @@ alternative_names:
 # arxiv:quant-ph/0210097
 
 description: |
-  A Galois-qudit code whose whose codespace consists of a direct sum of a Galois-qudit stabilizer codespace and one or more of that stabilizer code's error spaces.
+  A Galois-qubit code whose codespace consists of a direct sum of a Galois-qubit stabilizer codespace and one or more of that stabilizer code's error spaces.
 
-  The projection onto a stabilizer code is proportional to an equal sum over all elements of the stabilizer group \(\mathsf{S}\).
-  Union stabilizer codes generalize stabilizer codes by modifying the code projection with elements of a subset \(\mathsf{B}\subset\mathsf{S}\) called the \textit{Fourier description} \cite[Thm. 2.7]{arxiv:quant-ph/0210097}.
+  Given a subset \(T\) of coset representatives of \(\mathsf{N}(\mathsf{S})/\mathsf{S}\) of a Galois-qudit stabilizer code \(((n,K))\) with codespace \(\mathsf{C}\) and stabilizer group \(\mathsf{S}\), one can construct the Galois-qudit USt with codespace
+  \begin{align}
+    \mathsf{C}_{\text{USt}}=\bigoplus_{t\in T}t\mathsf{C}~.
+  \end{align}
+  The parameters of the USt are \(((n,K|T|,d))\), where \(|T|\) is the number of chosen coset representatives.
+  A Galois-qudit USt is \textit{CSS-like} when the underlying stabilizer code is CSS, so the coset representatives from the two classical codes underlying the CSS code.
+
+  Union stabilizer codes generalize stabilizer codes by modifying the original stabilizer code projection with elements of a subset \(\mathsf{B}\subset\mathsf{S}\) called the \textit{Fourier description} \cite[Thm. 2.7]{arxiv:quant-ph/0210097}.
   When \(\mathsf{B}\) is a subgroup of \(\mathsf{S}\), then the code reduces to an ordinary stabilizer code.
-  This construction is equivalent to that from Ref. \cite{arxiv:0801.2144}, as noted at the end of \cite[Sec. III]{arxiv:0801.2144}.
 
   The \(((n, \lceil\frac{q^n}{n(q^2-1)}\rceil,2))_q\) family of Galois-qudit non-stabilizer codes is constructed in Ref. \cite{arxiv:quant-ph/0210097}.
 
+# This construction is equivalent to that from Ref. \cite{arxiv:0801.2144}, as noted at the end of \cite[Sec. III]{arxiv:0801.2144}.
+
 #    Asymptotically good union stabilizer codes admitting efficient encoding and decoding procedures have been constructed.
 #    A technical definition for non-Galois qudits is as follows. For any \(\alpha\)-good \(n\times n\) matrix over \(\mathbb{F}_q\) and
 #    any \(\lfloor\alpha n\rfloor\)-pure maximal Gottesman subgroup of the error group \(\mathsf{E}, 0<\alpha<1\),
@@ -36,8 +43,7 @@ description: |
 
 relations:
   parents:
-    - code_id: galois_cws
-      detail: 'Galois-qudit union stabilizer codes can be defined as Galois-qudit CWS codes \cite{arxiv:0907.2038,manual:{Li, Yunfan. Codeword Stabilized Quantum Codes and Their Error Correction. Diss. UC Riverside, 2010.}}\cite[Sec. 10.4]{doi:10.1017/CBO9781139034807.012}.'
+    - code_id: galois_into_galois
 
 
 # Begin Entry Meta Information
diff --git a/codes/quantum/qudits_galois/stabilizer/evaluation/binary_quantum_goppa.yml b/codes/quantum/qudits_galois/stabilizer/evaluation/binary_quantum_goppa.yml
index 7b99fb38f..c3add9485 100644
--- a/codes/quantum/qudits_galois/stabilizer/evaluation/binary_quantum_goppa.yml
+++ b/codes/quantum/qudits_galois/stabilizer/evaluation/binary_quantum_goppa.yml
@@ -7,7 +7,7 @@ code_id: binary_quantum_goppa
 physical: galois
 logical: galois
 
-name: 'Binary quantum Goppa code'
+name: 'Quantum Goppa code'
 introduced: '\cite{arxiv:quant-ph/0501074,doi:10.1007/s11128-006-0047-9}'
 
 description: |
diff --git a/codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml b/codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml
index f5fbf7f2c..73674fb8e 100644
--- a/codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml
+++ b/codes/quantum/qudits_galois/stabilizer/galois_stabilizer.yml
@@ -13,7 +13,10 @@ introduced: '\cite{doi:10.1109/18.959288,arXiv:quant-ph/0508070}'
 description: |
   An \(((n,K,d))_q\) Galois-qudit code whose logical subspace is the joint eigenspace of commuting Galois-qudit Pauli operators forming the code's stabilizer group \(\mathsf{S}\). Traditionally, the logical subspace is the joint \(+1\) eigenspace, and the stabilizer group does not contain \(e^{i \phi} I\) for any \(\phi \neq 0\). The distance \(d\) is the minimum weight of a Galois-qudit Pauli string that implements a nontrivial logical operation in the code.
 
-  A Galois-qudit stabilizer code encoding an integer number of qudits (\(K=q^k\)) is denoted as \([[n,k]]_q\) or \([[n,k,d]]_q\). This notation differentiates between Galois-qudit and modular-qudit \([[n,k,d]]_{\mathbb{Z}_q}\) stabilizer codes, although the same notation is usually used for both. Galois-qudit stabilizer codes need not encode an integer number of qudits, with \(K=q^{n-\frac{r}{m}}\), where \(r\) is the number of generators of the stabilizer group, and \(q=p^m\) given prime \(p\) for all Galois qudits. As a result, \([[n,k,d]]\) notation is often used with non-integer \(k=\log_q K\).
+  A Galois-qudit stabilizer code encoding an integer number of qudits (\(K=q^k\)) is denoted as \([[n,k]]_q\) or \([[n,k,d]]_q\).
+  This notation differentiates between Galois-qudit and modular-qudit \([[n,k,d]]_{\mathbb{Z}_q}\) stabilizer codes, although the same notation is usually used for both.
+  Galois-qudit stabilizer codes need not encode an integer number of qudits, with \(K=q^{n-\frac{r}{m}}\), where \(r\) is the number of generators of the stabilizer group, and \(q=p^m\) given prime \(p\) for all Galois qudits.
+  As a result, \([[n,k,d]]\) notation is often used with non-integer \(k=\log_q K\).
 
   \begin{defterm}{Galois symplectic representation}
   \label{topic:galois-symplectic-representation}
@@ -68,9 +71,12 @@ notes:
 relations:
   parents:
     - code_id: galois_non_stabilizer
-      detail: 'A Galois-qudit union stabilizer code reduces to a Galois-qudit stabilizer code when there are no error spaces included in the code.'
+      detail: 'A Galois-qudit stabilizer code with stabilizer group \(\mathsf{S}\) can be thought of as a Galois-qudit USt with no coset representatives.
+      Conversely, if \(K = q^k\), and if the set of coset representatives of a Galois-qudit USt form a \(q\)-ary linear code, then they can be absorbed into a Galois-qudit stabilizer group that defines the USt.'
     - code_id: stabilizer
   cousins:
+    - code_id: galois_cws
+      detail: 'Galois-qudit CWS codes whose underlying classical code is a linear \(q\)-ary code are Galois-qudit stabilizer codes containing a cluster-state codeword.'
     - code_id: qudit_stabilizer
       detail: 'Recalling that \(q=p^m\), Galois-qudit stabilizer codes can also be treated as prime-qudit stabilizer codes on \(mn\) qudits, giving \(k=nm-r\) \cite{doi:10.1109/18.959288}. The case \(m=1\) reduces to conventional prime-qudit stabilizer codes on \(n\) qudits.'
     - code_id: q-ary_additive
diff --git a/codes/quantum/qudits_galois/stabilizer/qldpc/algebraic/2bga.yml b/codes/quantum/qudits_galois/stabilizer/qldpc/algebraic/2bga.yml
index a44c426dd..28a190898 100644
--- a/codes/quantum/qudits_galois/stabilizer/qldpc/algebraic/2bga.yml
+++ b/codes/quantum/qudits_galois/stabilizer/qldpc/algebraic/2bga.yml
@@ -29,8 +29,8 @@ description: |
     a u+v b=0,
   \end{align}
   with any two pairs \((u,v)\) and \((u',v')\) such that \(u'=u+w b\)
-  and \(v'=v-aw\) considered equivalent.  The order in the products is relevant
-  when the group is non-Abelian.
+  and \(v'=v-aw\) considered equivalent.
+  The order in the products is relevant when the group is non-Abelian.
 
   For example, consider the
   alternating group \(G=A_4=T\), also known as the rotation group of a