ref - lca

Author: valbert4

codes/quantum/groups/lca/lca_stabilizer.yml

@@ -48,6 +48,8 @@ relations:
       detail: 'Linear binary codes can be used to construct LCA stabilizer codes \cite{arxiv:2508.04819}.'
     - code_id: eeight
       detail: 'Integer symplectic matrices like the symplectic \(E_8\) generator matrix \cite[Appx. 2]{doi:10.1007/BF01232233} can be used to construct LCA stabilizer codes \cite{arxiv:2508.04819}.'
+    - code_id: group_gkp
+      detail: 'Simple single-mode single-qudit LCA codes are group-GKP codes with \(Kq \mathbb{Z} \subset \mathbb{Z} \subset \mathbb{R} \times \mathbb{Z}_q\), where \(K | q\) is the logical dimension \cite{arxiv:2508.04819}.'
 
 
 # Begin Entry Meta Information

codes/quantum/groups/nonabelian_stabilizer/group_gkp/group_gkp.yml

@@ -40,12 +40,12 @@ description: |
   Rotor GKP codes correspond to the \(\mathbb{Z}_{k_1} \subseteq \mathbb{Z}_{k_2} \subset U(1)\) group construction, where \(k=k_2/k_1\).
   \begin{table}
     \begin{cells}
-    \celldata<c H, c H, c H, l H>{Space & \(G\) & \(H\) & Related code}
+    \celldata<c H, c H, c H, l H>{Space & \(G\) & \(K\) & Related code}
     \celldata<c, c, c, l>{
     \(n\) qubits & \(\mathbb{Z}_2^n\) & \(\mathbb{Z}_2^m\)
         & qubit CSS
         \\
-    \(n\) modular qudits & \(\mathbb{Z}_q^n\) & \(H\)
+    \(n\) modular qudits & \(\mathbb{Z}_q^n\) & \(K\)
         & modular-qudit CSS
         \\
     \(n\) Galois qudits & \(\mathbb{F}_q^n\) & \(\mathbb{F}_q^m\)
@@ -66,8 +66,11 @@ description: |
     rotor & \(U(1)\) & \(\mathbb{Z}_n\)
         & rotor GKP
         \\
-    rigid body & \(SO(3)\) & \(H\)
+    rigid body & \(SO(3)\) & \(K\)
         & molecular
+        \\
+    1 mode, 1 qudit & \( \mathbb{R} \times \mathbb{Z}_q \) & \( \mathbb{Z} \)
+        & simple LCA
     }
     \end{cells}
     \caption{

codes/quantum/qudits/stabilizer/single_qudit/qudit_gkp.yml

@@ -19,7 +19,7 @@ description: |
   Modular-qudit analogue of the GKP code.
   Encodes a qudit into a larger qudit and protects against Pauli shifts up to some maximum value.
 
-  The simplest example requires a 15-dimensional qudit and admits stabilizer generators \(Z^6\) and \(X^6\).
+  The simplest example requires an 18-dimensional qudit and admits stabilizer generators \(Z^6\) and \(X^6\).
   The logical codewords are
   \begin{align}
   \begin{split}