galois_duadic

codes/classical/q-ary_digits/group/cyclic/q-ary_duadic.yml

@@ -11,7 +11,8 @@ name: '\(q\)-ary duadic code'
 introduced: '\cite{doi:10.1016/0097-3165(86)90066-X,doi:10.1007/978-3-7091-2786-5_1,doi:10.7907/CZA5-PX53,doi:10.1109/TIT.1987.1057300}'
 
 description: |
-  Member of a pair of cyclic linear binary codes that satisfy certain relations, depending on whether the pair is \textit{even-like} or \textit{odd-like} duadic. Duadic codes exist only when \(q\) is a square modulo \(n\) \cite{doi:10.1007/978-3-7091-2786-5_1}.
+  Member of a pair of cyclic linear binary codes that satisfy certain relations, depending on whether the pair is \textit{even-like} or \textit{odd-like} duadic.
+  Duadic codes exist only when \(q\) is a square modulo \(n\) \cite{doi:10.1007/978-3-7091-2786-5_1}.
 
   Duadic codes come in two pairs, an even-like duadic pair and an odd-like duadic pair. All codewords in the respective pairs are \textit{even-like}, i.e., \(\sum_i c_i = 0\), or \textit{odd-like}, i.e., \(\sum_i c_i \neq 0\). A code with all even-like (odd-like) codewords is called even-like (odd-like).
 

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

@@ -0,0 +1,35 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+
+code_id: galois_duadic
+physical: galois
+logical: galois
+
+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.
+
+
+relations:
+  parents:
+    - code_id: galois_true_stabilizer
+      detail: 'Quantum duadic codes can be constructed via the CSS construction or the Hermitian construction.'
+  cousins:
+    - code_id: q-ary_duadic
+    - code_id: galois_css
+      detail: 'Quantum duadic codes can be constructed via the CSS construction or the Hermitian construction.'
+    - code_id: stabilizer_over_gfqsq
+      detail: 'Quantum duadic codes can be constructed via the CSS construction or the Hermitian construction.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-05-05'

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

@@ -19,6 +19,8 @@ description: |
 relations:
   parents:
     - code_id: galois_css
+    - code_id: galois_duadic
+      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.'