From 09aa6b6199821100cf5acfd54e2f42e3ab5f4e2d Mon Sep 17 00:00:00 2001 From: LeonidPryadko <63686094+LeonidPryadko@users.noreply.github.com> Date: Tue, 17 Oct 2023 12:25:08 -0700 Subject: [PATCH 1/2] Update 2bga.yml small edits in two places --- codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml b/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml index 28679b016..de033ef68 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 \(v'=v-aw\) are considered equivalent. The order in the products is relevant when the group is non-Abelian. For example, consider the From 7ad63b14af99129a056b2f93e04b514ac12fd9f6 Mon Sep 17 00:00:00 2001 From: LeonidPryadko <63686094+LeonidPryadko@users.noreply.github.com> Date: Tue, 17 Oct 2023 12:36:33 -0700 Subject: [PATCH 2/2] typo fixed --- codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml b/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml index de033ef68..e348ce648 100644 --- a/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml +++ b/codes/quantum/qudits_galois/qldpc/algebraic/2bga.yml @@ -26,7 +26,7 @@ description: | a u+v b=0, \end{align} with any two pairs \((u,v)\) and \((u',v')\) such that \(u'=u+w b\) - and \(v'=v-aw\) are considered equivalent. 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