~

Author: valbert4

codes/quantum/qubits/small_distance/small/10/xzzx_10_2_3.yml

@@ -47,16 +47,13 @@ relations:
       detail: 'This is the \(d=3\) instance of the \([[d^2+1,2,d]]\) family of twisted XZZX toric codes
         (parameters \(a=1\), \(b=3\)), presented in its CSS form \cite{arxiv:2509.06865}.'
     - code_id: bipartite_cyclic_cluster
-      detail: 'The \([[10,2,3]]\) rotated toric code is a \([[d^2+1,2,d]]\) BCC code for \(d=3\) \cite{arxiv:2509.06865}.'
+      detail: 'The \([[10,2,3]]\) rotated toric code is a \([[d^2+1,2,d]]\) BCC code for \(d=3\) \cite{arxiv:2509.06865}. A non-CSS cyclic cluster code related to the \([[10,2,3]]\) rotated toric code yields the \([[5,1,3]]\) five-qubit perfect code for \(d=3\) \cite{arxiv:2509.06865}.'
     - code_id: small_distance_qubit_stabilizer
   cousins:
     - code_id: stab_5_1_3
       detail: 'The \([[10,2,3]]\) rotated toric code is the \hyperref[topic:symplectic-doubling]{symplectic double} (a.k.a. genus-one double cover) of the five-qubit perfect code \cite[Exam. 3]{arxiv:1212.6703}\cite{arxiv:2406.09951}. A non-CSS cyclic cluster code related to the \([[10,2,3]]\) rotated toric code yields the \([[5,1,3]]\) five-qubit perfect code for \(d=3\) \cite{arxiv:2509.06865}.'
     - code_id: stab_5_1_2
       detail: 'The \([[10,2,3]]\) rotated toric code is the \hyperref[topic:symplectic-doubling]{symplectic double} (a.k.a. genus-one double cover) of the \([[5,1,2]]\) rotated surface code \cite{arxiv:2406.09951}.'
-    - code_id: bipartite_cyclic_cluster
-      detail: 'A non-CSS cyclic cluster code related to the \([[10,2,3]]\) rotated toric code yields the \([[5,1,3]]\) five-qubit perfect code for \(d=3\) \cite{arxiv:2509.06865}.'
-
 
 
 # Begin Entry Meta Information

codes/quantum/qubits/small_distance/small/12/css_12_1_3.yml

@@ -17,7 +17,7 @@ description: |
 
   One stabilizer tableau for the code is, up to Pauli frame \cite{arxiv:2507.10395},
   \begin{align}
-  \begin{smallmatrix}
+  \begin{array}{cccccccccccc}
     X & X & X & X & I & I & I & I & I & I & I & I \\
     I & I & X & X & X & X & I & I & I & I & I & I \\
     I & I & I & I & I & I & X & X & X & X & I & I \\
@@ -29,7 +29,7 @@ description: |
     I & I & I & I & I & I & Z & Z & I & I & I & I \\
     I & I & I & I & I & I & I & I & Z & Z & I & I \\
     I & I & I & I & I & I & I & I & I & I & Z & Z
-  \end{smallmatrix}~.
+  \end{array}~.
   \end{align}
 
 protection: |