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arXiv · 2210.08716

On construction of quantum codes with dual-containing quasi-cyclic codes

Chaofeng Guan·Ruihu Li·Liangdong Lu·Yang Liu·Hao Song
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Abstract

One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the construction of quantum codes over small fields. Firstly, some sufficient conditions for these 2-generator quasi-cyclic codes to be dual-containing concerning Hermitian inner product are determined. Then, we utilize these Hermitian dual-containing quasi-cyclic codes to produce quantum codes via the famous Hermitian construction. Moreover, we present a lower bound on the minimum distance of these quasi-cyclic codes, which is helpful to construct quantum codes with larger lengths and dimensions. As the computational results, many new quantum codes that exceed the quantum Gilbert-Varshamov bound are constructed over $F_q$, where $q$ is $2,3,4,5$. In particular, 16 binary quantum codes raise the lower bound on the minimum distance in Grassl's table \cite{Grassl:codetables}. In nonbinary cases, many quantum codes are new or have better parameters than those in the literature.

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Chaofeng Guan, Ruihu Li, Liangdong Lu, Yang Liu, Hao Song. 2022-10-17. On construction of quantum codes with dual-containing quasi-cyclic codes. https://doi.org/10.1007/s11128-022-03621-7

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