diff --git a/codes/quantum/qudits_galois/qldpc/algebraic/generalized_bicycle.yml b/codes/quantum/qudits_galois/qldpc/algebraic/generalized_bicycle.yml index affcd9582..025563ee7 100644 --- a/codes/quantum/qudits_galois/qldpc/algebraic/generalized_bicycle.yml +++ b/codes/quantum/qudits_galois/qldpc/algebraic/generalized_bicycle.yml @@ -87,7 +87,7 @@ relations: The 2BGA code LP\((a,b)\) is then just a generalized bicycle code GB\([a(x),b(x)]\) constructed from the polynomials \(a(x)\) and \(b(x)\) corresponding to \(a,b\in \mathbb{F}_q[\mathbb{Z}_{\ell}]\). - code_id: lifted_product detail: | - A code GB\((a,b)\) with circulants of size \(\ell\) is a special (degenerate) case of a lifted-product code LP\((A,B)\) code over the Abelian \hyperref[topic:group-algebra]{group algebra} \(\mathbb{F}_q[\mathbb{Z}_{\ell}]\) associated with the cyclic group \(\mathbb{Z}_{\ell}\equiv \langle x|x^\ell=1\rangle\), with \(1\times 1\) matrices \(A=a(x)\), \(B=b(b)\) given by the corresponding polynomials. + A code GB\((a,b)\) with circulants of size \(\ell\) is a special (degenerate) case of a lifted-product code LP\((A,B)\) code over the Abelian \hyperref[topic:group-algebra]{group algebra} \(\mathbb{F}_q[\mathbb{Z}_{\ell}]\) associated with the cyclic group \(\mathbb{Z}_{\ell}\equiv \langle x|x^\ell=1\rangle\), with \(1\times 1\) matrices \(A=a(x)\), \(B=b(x)\) given by the corresponding polynomials. - code_id: quantum_quasi_cyclic detail: | An index-\(m\) quasi-cyclic (QC) code of length \(n=m\ell\) is usually defined as a linear code invariant under the \(m\)-step shift permutation \(T_{n}^{m}\).