Mod6

codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml

@@ -13,20 +13,20 @@ introduced: '\cite{arxiv:2305.06890,arXiv:2306.16400}'
 
 description: |
   2BGA codes are the smallest \hyperref[code:lifted_product]{LP codes}
-  LP\((a,b)\), constructed from a pair of \hyperref[topic:group-algebra]{group algebra} elements
+  LP\((a,b)\), \hyperref[topic:galois_css]{CSS codes} constructed from a pair of \hyperref[topic:group-algebra]{group algebra} elements
   \(a,b\in \mathbb{F}_q[G]\), where \(G\) is a finite group, and \(\mathbb{F}_q\) is a Galois field.
   For a group of order \(\ell\), we get a 2BGA code of length
   \(n=2\ell\).
   A 2BGA code for an Abelian group is called an \textit{Abelian 2BGA code}.
 
-  An \(\mathbb{F}_q\)-linear code isomorphic to a \(Z\)-part of the 2BGA code LP\((a,b)\) can be most
+  An \(\mathbb{F}_q\)-linear code isomorphic to a \(Z\) logical subspace of the 2BGA code LP\((a,b)\) can be most
   naturally defined as a linear space of pairs
   \((u,v)\in \mathbb{F}_q[G]\times \mathbb{F}_q[G]\) such that
   \begin{align}
     a u+v b=0,
   \end{align}
   with any two pairs \((u,v)\) and \((u',v')\) such that \(u'=u+w b\)
-  and \(v'=v-aw\) identified.  The order in the products is relevant
+  and \(v'=v-aw\) considered equivalent.  The order in the products is relevant
   when the group is non-Abelian.
 
   For example, consider the