refs

codes/classical/bits/easy/hamming/hamming.yml

@@ -44,7 +44,6 @@ relations:
     - code_id: extended_hamming
     - code_id: reed_muller
       detail: 'Binary Hamming codes are equivalent to RM\(^*(r-2,r)\).'
-    - code_id: quantum_hamming
     - code_id: nearly_perfect
       detail: 'Shortened Hamming codes \([2^r-2,2^r-r-2,3]\) are nearly perfect (\cite{preset:MacSlo}, pg. 533).'
 

codes/quantum/qubits/stabilizer/data_syndrome.yml

@@ -9,22 +9,23 @@ logical: qubits
 
 name: 'Quantum data-syndrome (DS) code'
 short_name: 'DS code'
-introduced: '\cite{arxiv:1409.2559,arxiv:1907.01393}'
+introduced: '\cite{arxiv:1409.2559,doi:10.1109/ISIT.2014.6874892,doi:10.1109/ISIT.2015.7282628,doi:10.1109/ISIT.2016.7541704,arxiv:1907.01393}'
 
 description: |
-  Stabilizer code designed to correct both data qubit errors and syndrome measurement errors simultaneously due to extra redundancy in their stabilizer generators.
+  Stabilizer code designed to correct both data qubit errors and syndrome measurement errors simultaneously due to extra redundancy in its stabilizer generators.
 
-  Extra redundancy can be added to any \([[n,n-m]]\) qubit stabilizer code by expanding its stabilizer generator matrix \(H\) as
+  The redundancy can be added to any \([[n,n-m]]\) qubit stabilizer code by expanding its stabilizer generator matrix \(H\) as
   \begin{align}
     H_{DS}=\begin{pmatrix}H & I_{m} & 0\\
     0 & A^{T} & I_{r}
     \end{pmatrix}~,
   \end{align}
-  where the redundancy is provided by the underlying \([m+r,m]\) \textit{syndrome measurement code} with generator matrix \(G= (I_m|A)\).
+  where the redundancy is provided by the underlying \([m+r,m]\) \textit{syndrome measurement code} with generator matrix \(G= (I_m|A)\) \cite{arxiv:1907.01393}.
 
 protection: |
   Protects against both physical qubit and syndrome measurement errors.
-  Singleton bounds, Hamming bounds, and \hyperref[topic:quantum-weight-enumerator]{quantum MacWilliams identities} can be extended to DS codes.
+  Quantum Singleton bounds, quantum Hamming bounds, and \hyperref[topic:quantum-weight-enumerator]{quantum MacWilliams identities} can be extended to DS codes.
+  Single-error-correcting DS codes stemming from \hyperref[topic:quantum-weight-enumerator]{impure} stabilizer codes must satisfy a variant of the quantum Hamming bound \cite{arxiv:2302.01527}.
 
 features:
   decoders:
@@ -39,14 +40,23 @@ relations:
     - code_id: qubit_stabilizer
       detail: 'Quantum DS codes are stabilizer codes whose stabilizer generators encode extra redundancy (via a linear binary code) so as to protect from syndrome measurement errors.'
   cousins:
-    - code_id: quantum_hamming
-      detail: 'Codes such as the quantum Hamming code can be expanded to DS codes using almost any good binary linear code because their stabilizer generators are all have the same weight \cite{arxiv:1907.01393}.'
+    - code_id: quantum_hamming_css
+      detail: 'Codes such as the quantum Hamming code can be expanded to DS codes using almost any good binary linear code because their stabilizer generators all have the same weight \cite{arxiv:1907.01393}.'
     - code_id: quantum_mds
-      detail: 'The quantum Singleton bound can be formulated for DS codes \cite{arxiv:1907.01393}.'
+      detail: 'The quantum Singleton bound can be extended to DS codes \cite{arxiv:1907.01393}.'
     - code_id: quantum_perfect
-      detail: 'The quantum Singleton bound can be formulated for DS codes \cite{arxiv:1907.01393}.'
+      detail: 'The quantum Hamming bound can be extended to DS codes \cite{arxiv:1907.01393}.'
     - code_id: binary_linear
       detail: 'The DS code construction employs a particular binary linear code to provide protection against syndrome measurement errors.'
+    - code_id: quantum_convolutional
+      detail: 'The DS code framework has been extended to quantum convolutional codes \cite{arxiv:1902.07395}.'
+    - code_id: single_shot
+      detail: 'DS codes contain redundancy in their stabilizer generators so as to protect from syndrome measurement errors.'
+    - code_id: bch
+      detail: 'Primitive narrow-sense BCH codes can be used as the syndrome measurement codes of a DS code \cite{arxiv:2311.16044}.
+      This construction requires fewer measurements than a previous general construction \cite{arxiv:1409.2559}.'
+    - code_id: qubit_subsystem
+      detail: 'The DS construction can be extended to qubit subsystem codes \cite{arxiv:2302.01527}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits/small/qutrit_golay.yml

@@ -39,7 +39,7 @@ relations:
   parents:
     - code_id: qudit_css
     - code_id: galois_quad_residue
-      detail: 'The qutrit Golay code is a qutrit quantum QR code sice the ternary Golay code is a QR code.'
+      detail: 'The qutrit Golay code is a qutrit quantum QR code since the ternary Golay code is a QR code.'
     - code_id: small_distance_quantum
   cousins:
     - code_id: ternary_golay

codes/quantum/qudits_galois/stabilizer/duadic/galois_duadic.yml

@@ -12,7 +12,7 @@ name: 'Quantum duadic code'
 introduced: '\cite{arxiv:quant-ph/0601117,arxiv:0711.2050,doi:10.1142/S0219749909004979,arxiv:2211.00891}'
 
 description: |
-  True \(q\)-Galois-qudit stabilizer code constructed from \(q\)-ary duadic codes via the Hermitian construction or the Galois-qudit CSS construction.
+  True Galois-qudit stabilizer code constructed from \(q\)-ary duadic codes via the Hermitian construction or the Galois-qudit CSS construction.
 
 
 relations:

codes/quantum/qudits_galois/stabilizer/duadic/galois_quad_residue.yml

@@ -23,7 +23,6 @@ relations:
       detail: 'Quantum QR codes are quantum duadic codes since QR codes are duadic codes.'
   cousins:
     - code_id: q-ary_quad_residue
-      detail: 'The qubit Golay code is a qubit quantum QR code sice the Golay code is a binary QR code.'
     - code_id: data_syndrome
       detail: 'A family of qubit quantum QR codes can be made into DS codes \cite[Thm. 14]{arxiv:1907.01393}.'
     - code_id: quantum_mds