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Quantum two-block group algebra codes

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arxiv 2306.16400 v1 pith:F2A5RNXM submitted 2023-06-28 quant-ph math-phmath.MP

classification quant-phmath-phmath.MP
keywords codesgroupgroupsquantumabelianalgebraclassicalnon-abelian
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We consider quantum two-block group algebra (2BGA) codes, a previously unstudied family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle (GB) codes, except a cyclic group is replaced with an arbitrary finite group, generally non-abelian. As special cases, 2BGA codes include a subset of square-matrix LP codes over abelian groups, including quasi-cyclic codes, and all square-matrix hypergraph-product codes constructed from a pair of classical group codes. We establish criteria for permutation equivalence of 2BGA codes and give bounds for their parameters, both explicit and in relation to other quantum and classical codes. We also enumerate the optimal parameters of all inequivalent connected 2BGA codes with stabilizer generator weights $W \le 8$, of length $n \le 100$ for abelian groups, and $n \le 200$ for non-abelian groups.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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    quant-ph 2026-01 conditional novelty 5.0 of 10

    Koszul complexes built from four polynomial generators over cyclic group rings yield CSS codes with both X and Z metachecks, giving small, high-confinement, single-shot-decodable quantum codes.

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