@@ -23,6 +23,10 @@ description: |
   A different BB QLDPC code with the same parameters was introduced in \cite{arxiv:2407.16336}.
 # https://twitter.com/jaygambetta/status/1773099803561381995
 
+protection: |
+  Up to equivalence, the gross code is the only qubit \hyperref[code:abelian_2bga]{Abelian 2BGA code} with check weight six and \(n\leq 200\) that reaches \(kd^2/n=12\) \cite{arxiv:2610.13880}.
+  It has the largest \(kd^2/n\) among all qubit 2BGA codes with check weight six and \(n\leq 191\) \cite{arxiv:2610.13880}.
+
 features:
   rate: 'An ancilla-added rate of \(1/24\). In contrast, the distance-13 surface code has ancilla-added rate \(1/338\).'
   # 12 logical qubits would require nearly 3000 physical qubits with separate surface-code patches in the comparison of Ref. \cite{arxiv:2308.07915}.
@@ -69,6 +73,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: AnthonyLeverrier
       date: '2026-07-22'
     - user_id: VictorVAlbert
 
@@ -52,6 +52,9 @@ protection: |
   Some upper and lower bounds on parameters and many examples of 2BGA codes are given in Ref. \cite{arxiv:2306.16400}.
   When the support groups generated by \(a\) and \(b\) intersect trivially, the code is equivalent to a square-matrix Galois-qudit hypergraph-product code and its distance reduces to \(d=\min(d_A^{\perp},d_B^{\perp})\); classical finite-rate group-algebra codes therefore yield finite-rate 2BGA families with \(d=\mathcal{O}(n^{1/2})\) \cite{arxiv:2306.16400}.
 
+  A qubit 2BGA code in which \(a\) or \(b\) is a unit of \(\mathbb{F}_2[G]\) has \(k=0\) \cite[Prop. C.1]{arxiv:2610.13880}, generalizing the Abelian case \cite[Cor. 2.6]{arxiv:2407.03973}.
+  In particular, a qubit 2BGA code over a 2-group has \(k=0\) whenever \(a\) or \(b\) has odd weight, since such elements of \(\mathbb{F}_2[G]\) are units \cite[Prop. C.1]{arxiv:2610.13880}.
+
 features:
   transversal_gates:
     - 'Logical Pauli operators and fold-transversal gates have been studied \cite{arxiv:2407.03973,arxiv:2409.18175}.'
@@ -75,6 +78,7 @@ features:
 notes:
   - 'The idea of generating stabilizers according to a Cayley graph of a group was independently proposed by Hastings \cite{manual:{M. B. Hastings, LR codes, private communication, 2014}}; see Ref. \cite{arxiv:1812.02101}, which contains an error in Prop. 3.2 \cite{manual:{H.-K. Lin and L. P. Pryadko, private communication, 2024}}.'
   - 'A database of 2BGA codes is available in QECDB \cite{preset:QECDB}.'
+  - 'A database of about \(12{,}400\) qubit 2BGA codes with \(n\leq 320\), check weights five to nine, and exact distances is available at \href{https://github.com/gideonlsx/bicycle-race}{bicycle-race} \cite{arxiv:2610.13880}.'
 
 
 relations:
@@ -111,6 +115,8 @@ relations:
 _meta:
   # Change log - most recent first
   changelog:
+    - user_id: VictorVAlbert
+      date: '2026-10-12'
     - user_id: VictorVAlbert
       date: '2026-08-22'
     - user_id: VictorVAlbert