Related papers: Abelian and non-abelian quantum two-block codes

Abelian and non-abelian quantum two-block codes

URL: http://arxiv.org/abs/2305.06890v2
Date: Mon, 31 Jul 2023 00:45:52 GMT
Title: Abelian and non-abelian quantum two-block codes
Authors: Renyu Wang, Hsiang-Ku Lin, and Leonid P. Pryadko
Abstract summary: Two-block group-algebra (2BGA) codes, where a cyclic group is replaced with an arbitrary finite group, generally non-abelian. This gives a simple criterion for an essentially non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a code based on an abelian group. We also give a lower bound on the distance which, in particular, applies to the case when a 2BGA code reduces to a hypergraph-product code constructed from a pair of classical group codes.
Score: 0.5658568324275767
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices.Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic group is replaced with an arbitrary finite group, generally non-abelian. We present code construction and give several expressions for code dimension, applicable depending on whether the constituent group is cyclic, abelian, or non-abelian. This gives a simple criterion for an essentially non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a code based on an abelian group. We also give a lower bound on the distance which, in particular, applies to the case when a 2BGA code reduces to a hypergraph-product code constructed from a pair of classical group codes.

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