complex_hadamard

codes/classical/bits/combinatorial_design.yml

@@ -34,7 +34,7 @@ description: |
 
 
 notes:
-  - 'See \cite{preset:HKSdesigns} for a review on combinatorial designs.'
+  - 'See \cite{doi:10.1090/surv/175,preset:HKSdesigns} for reviews on combinatorial designs.'
   - 'See \cite{doi:10.1017/CBO9780511549533,doi:10.1201/9781420010541,doi:10.1017/CBO9780511623714,doi:10.1007/b97564} for books on combinatorial designs.'
 
 relations:
@@ -77,7 +77,7 @@ relations:
       detail: 'Some Steiner systems can be used to construct Gallager codes \cite{doi:10.1007/978-1-4613-0165-3_6}.'
     - code_id: algebraic_ldpc
       detail: 'Combinatorial designs can be used to construct explicit LDPC codes \cite{doi:10.1109/ITW.2001.955146,doi:10.1109/GLOCOM.2001.965562,doi:10.1109/TCOMM.2003.816946}.'
-    - code_id: biorthogonal
+    - code_id: hadamard
       detail: '\textit{Hadamard designs} form a set of combinatorial designs that are equivalent to Hadamard matrices \cite{doi:10.1002/sapm1933121321}; see Ref. \cite{doi:10.1201/9781420010541}.'
 
 

codes/classical/bits/easy/dual_hamming/hadamard.yml

@@ -19,6 +19,9 @@ description: |
   The \([2^m,m+1,2^{m-1}]\) augmented Hadamard code is the first-order RM code (a.k.a. RM\((1,m)\)), while the \([2^m-1,m,2^{m-1}]\) shortened Hadamard code is the simplex code (a.k.a. RM\(^*(1,m)\)).
 
 
+notes:
+  - 'Review of Hadamard matrices \cite{doi:10.1214/aos/1176344370}.'
+
 relations:
   parents:
     - code_id: binary_ltc

codes/classical/spherical/q-ary/complex_hadamard.yml

@@ -0,0 +1,36 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: complex_hadamard
+physical: spheres
+logical: reals
+
+name: 'Complex Hadamard spherical code'
+introduced: '\cite{arxiv:2311.00354}'
+
+description: |
+  A spherical code obtained from particular complex Hadamard matrices \cite{arxiv:2309.07522}.
+
+protection: |
+  Covering radius can be bounded in terms of the code's spherical design strength \cite{arxiv:2311.00354}.
+
+
+notes:
+  - 'Database of complex Hadamard matrices \cite{arXiv:quant-ph/0512154}.'
+
+relations:
+  parents:
+    - code_id: spherical
+  cousins:
+    - code_id: stabilizer_over_gfqsq
+      detail: 'Complex Hadamard matrices can be used to build Hermitian Galois-qudit codes \cite{arxiv:2309.07522}.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-07-07'

codes/quantum/properties/block/tensor_network/holographic_tensor.yml

@@ -62,5 +62,7 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: MatthewSteinberg
+      date: '2024-07-01'
     - user_id: VictorVAlbert
       date: '2024-07-01'

codes/quantum/qubits/stabilizer/holographic/holographic_steane.yml

@@ -15,14 +15,15 @@ alternative_names:
 
 description: |
   Holographic tensor-network code constructed out of a network of encoding isometries of the Steane code.
+  Depending on how the isometry tensors are contracted, there is a zero-rate and a finite-rate code family.
 
 features:
   decoders:
     - 'Optimal erasure decoder \cite{arxiv:1806.06472}.'
 
   threshold:
-    - '\(~33\%\) under erasure noise using optimal erasure decoder \cite{arxiv:1806.06472}.'
-    - '\(9.4\%\) under depolarizing noise using tensor-network decoder \cite{arxiv:2012.07317}.'
+    - '\(~33\%\) under erasures using optimal erasure decoder for the finite-rate family, and \(50\%\) for the zero-rate family \cite{arxiv:1806.06472}.'
+    - 'Depolarizing noise: \(9.4\%\) using tensor-network decoder, and \(\sim 7\%\) using integer optimization decoder \cite{arxiv:2012.07317}.'
 
 
 relations:

codes/quantum/qudits_galois/stabilizer/stabilizer_over_gfqsq.yml

@@ -27,6 +27,7 @@ protection: |
   There is an isomorphism between the symplectic and \(GF(q^2)\) representations \cite[Thm. 27.3.8]{preset:HKSquantum}.
 
   It has also been extended to \(q^{2m}\)-ary Hermitian self-orthogonal linear codes \cite{arxiv:2012.11998}, and similar constructions were formulated in Ref. \cite{arxiv:1002.4088}.
+  Construction X and XX have also been adapted to yield quantum codes \cite{doi:10.1007/s10623-014-9934-8}.
 
 
 #   and later proven via the \hyperref[code:stabilizer_over_gfqsq]{Hermitian construction} (showing self-orthogonality under the trace-alternating inner product; see Ref. \cite[Corr. 19]{arxiv:quant-ph/0508070}, ).

users/users_db.yml

@@ -34,7 +34,9 @@
 
 
 #
-
+- user_id: MatthewSteinberg
+  name: 'Matthew Steinberg'
+  gscholaruser: lGZwMRAAAAAJ
 
 - user_id: GregKuperberg
   name: 'Greg Kuperberg'