tenfold code + refs

codes/quantum/groups/group_10_1_4.yml

@@ -0,0 +1,31 @@
+#######################################################
+## This is a code entry in the error correction zoo. ##
+##       https://github.com/errorcorrectionzoo       ##
+#######################################################
+
+code_id: group_10_1_4
+physical: groups
+logical: groups
+
+name: 'Tenfold code'
+introduced: '\cite[Prop. V.1]{arXiv:quant-ph/0012111}'
+
+description: |
+  \([[10,1,4]]_{G}\) Abelian group code that is defined using a graph that is closely related to the \([[5,1,3]]\) code.
+
+relations:
+  parents:
+    - code_id: group_quantum
+    - code_id: small_distance_quantum
+  cousins:
+    - code_id: qudit_5_1_3
+      detail: 'The \([[10,1,4]]_{G}\) Abelian group code is defined using a graph that is closely related to the \([[5,1,3]]\) code.'
+
+
+# Begin Entry Meta Information
+_meta:
+  # Change log - most recent first
+  changelog:
+    - user_id: VictorVAlbert
+      date: '2024-02-24'
+

codes/quantum/properties/block/small_distance_quantum.yml

@@ -11,7 +11,8 @@ name: 'Small-distance block quantum code'
 description: |
   A block quantum code on \(n\) subsystems that either detects or corrects errors on at most two subsystems, i.e., have distance \(\leq 5\).
 
-  All single error-correcting qubit stabilizer codes have been classified \cite{arxiv:0901.1968}. See Refs. \cite{arxiv:quant-ph/9704043,arxiv:0801.0831} for other small-distance stabilizer codes.
+  All single error-correcting qubit stabilizer codes have been classified \cite{arxiv:0901.1968}.
+  See Refs. \cite{arxiv:quant-ph/9704043,arxiv:0801.0831} for other small-distance stabilizer codes.
 
 relations:
   parents:

codes/quantum/qubits/small_distance/small/stab_8_3_3.yml

@@ -17,6 +17,7 @@ description: |
 
    See \cite[Table 3.3]{arxiv:quant-ph/9705052} for its stabilizer generator matrix.
    The code's automorphism group is \(\text{A}\Gamma\text{L}(1,8)\) \cite{arxiv:2109.12735}.
+   It is unique for its parameters, up to local equivalence \cite{arxiv:0709.1780}.
 
 
 relations:

codes/quantum/qubits/small_distance/small/steane.yml

@@ -37,7 +37,9 @@ description: |
     |\overline{0}\rangle&=\frac{1}{\sqrt{8}}\Big(|0000000\rangle+|1010101\rangle+|0110011\rangle+|1100110\rangle\\&\,\,\,\,\,\,\,\,+|0001111\rangle+|1011010\rangle+|0111100\rangle+|1101001\rangle\Big)\\|\overline{1}\rangle&=\frac{1}{\sqrt{8}}\Big(|1111111\rangle+|0101010\rangle+|1001100\rangle+|0011001\rangle\\&\,\,\,\,\,\,\,\,+|1110000\rangle+|0100101\rangle+|1000011\rangle+|0010110\rangle\Big)~.
   \end{split}
   \end{align}
+
   The automorphism group of the code is \(PGL(3,2)\) \cite{arxiv:2109.12735}.
+  It is one of ten distinct \([[7,1,3]]\) codes \cite{arxiv:0709.1780}.
 
 protection: 'The Steane code is a distance 3 code. It detects errors on 2 qubits, corrects errors on 1 qubit.'