@@ -24,9 +24,8 @@ description: |
 # https://twitter.com/jaygambetta/status/1773099803561381995
 
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-  Up to equivalence, the gross code is the only \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}.
-  Over all groups, it has the largest \(kd^2/n\) among qubit 2BGA codes with check weight six and \(n\leq 191\) \cite{arxiv:2610.13880}.
-  It is first exceeded at \(n=192\) by a non-Abelian \([[192,12,14]]\) 2BGA code \cite{arxiv:2306.16400,arxiv:2610.13880}.
+  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 \(1/338\).'
 
@@ -52,8 +52,8 @@ 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}.
-  Over a 2-group, the units of \(\mathbb{F}_2[G]\) are exactly the elements of odd weight, so any block of odd weight forces \(k=0\) \cite[Prop. C.1]{arxiv:2610.13880}.
+  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:
@@ -78,7 +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 \(n\leq 320\) and check weights five to nine is available at \href{https://github.com/gideonlsx/bicycle-race}{bicycle-race} \cite{arxiv:2610.13880}. Every code in it has an exact distance and a logical operator of that weight. The database also holds a set of \(2{,}611\) published QLDPC codes with \(n\leq 1000\), with their parameters and sources \cite[App. E]{arxiv:2610.13880}.'
+  - '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}.'
 
 
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