diff --git a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml b/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml index 28679b016..e348ce648 100644 --- a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml +++ b/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