~

codes/quantum/qubits/nonstabilizer/cws/non_stabilizer.yml

@@ -8,17 +8,17 @@ physical: qubits
 logical: qubits
 
 name: 'Union stabilizer code'
-introduced: '\cite{arXiv:quant-ph/9703016,arxiv:quant-ph/0210097,arxiv:0801.2144}'
+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
 
 alternative_names:
   - 'Non-stabilizer code'
 # arxiv:quant-ph/0210097
 
 description: |
-  Extension of stabilizer codes whose codespace consists of a direct sum of a stabilizer codespace and one or more of that stabilizer code's error spaces.
+  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.
 
-  Union stabilizer codes constructed in Ref. \cite{arxiv:quant-ph/0210097} include \(((33, 155, 3))\), \(((15, 8, 3))\).
+  Union stabilizer codes constructed in Ref. \cite{arxiv:quant-ph/0210097} include the \(((33, 155, 3))\) and \(((15, 8, 3))\) codes.
 
 
 features:

codes/quantum/qubits/nonstabilizer/cws/quantum_goethals_preparata.yml

@@ -16,18 +16,20 @@ description: |
   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}.
 
   The Goethals and Preparata codes can each be used to obtain families of union stabilizer codes with distance 8 and 6, respectively \cite{arxiv:0801.2144}.
-  Plugging the \(\mathbb{Z}_4\) versions of these codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.
+  A construction using the \(\mathbb{Z}_4\) versions of these codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.
 
 relations:
   parents:
-    - code_id: cws
+    - code_id: non_stabilizer
   cousins:
     - code_id: goethals
+      detail: 'The \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code is constructed using the classical Goethals and Preparata codes \cite{arXiv:0801.2144,arxiv:0801.2150}.
+      A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.'
     - code_id: preparata
+      detail: 'The \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code is constructed using the classical Goethals and Preparata codes \cite{arXiv:0801.2144,arxiv:0801.2150}.
+      A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.'
     - code_id: gray
-      detail: 'Plugging the \(\mathbb{Z}_4\) versions of the Kerdock and Preparate codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata codes \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.'
-    - code_id: qudit_css
-      detail: 'Plugging the \(\mathbb{Z}_4\) versions of the Kerdock and Preparate codes into the modular-qudit CSS construction and applying the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata codes \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.'
+      detail: 'A construction using the \(\mathbb{Z}_4\) versions of the Goethals and Preparata codes and the Gray map yields qubit code families with similar parameters as the \(((2^m,2^{2^m−5m+1},8))\) Goethals-Preparata code \cite{manual:{S. Ling and P. Sole. 2008. Nonadditive quantum codes from Z4-codes. http://hal.archives-ouvertes.fr/hal-00338309/fr/.}}.'
 
 
 

codes/quantum/qubits/nonstabilizer/cws/qubit_5_6_2.yml

@@ -24,7 +24,7 @@ relations:
       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/0210097}.'
+      detail: 'The six-qubit CWS code is a union stabilizer code \cite{arXiv:quant-ph/9703002,arxiv:quant-ph/0210097}.'
 
 
 # Begin Entry Meta Information

codes/quantum/qudits_galois/nonstabilizer/galois_non_stabilizer.yml

@@ -8,15 +8,15 @@ physical: galois
 logical: galois
 
 name: 'Galois-qudit union stabilizer code'
-introduced: '\cite{arXiv:quant-ph/9703016,arxiv:quant-ph/0210097,arxiv:0801.2144}'
+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
 
 alternative_names:
   - 'Galois-qudit non-stabilizer code'
 # arxiv:quant-ph/0210097
 
 description: |
-  Extension of Galois-qudit stabilizer codes 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-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.
 
   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}.