2023/06/28 by Hsiang-Ku Lin, Leonid P. Pryadko, Lin, Hsiang-Ku +1 · 13 citations
Computer Science · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2306.16400
openalex publication_date 2023/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≤ 8, of length n ≤ 100 for abelian groups, and n ≤ 200 for non-abelian groups.