Two classes of constacyclic codes with a square-root-like lower bound

Tingfang Chen; Zhonghua Sun; Conghui Xie; Hao Chen; Cunsheng Ding

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arXiv · 2404.18438

Two classes of constacyclic codes with a square-root-like lower bound

Tingfang Chen·Zhonghua Sun·Conghui Xie·Hao Chen·Cunsheng Ding

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Abstract

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this paper, an infinite class of $q$-ary negacyclic codes of length $(q^m-1)/2$ and an infinite class of $q$-ary constacyclic codes of length $(q^m-1)/(q-1)$ are constructed and analyzed. As a by-product, two infinite classes of ternary negacyclic self-dual codes with a square-root-like lower bound on their minimum distances are presented.

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Tingfang Chen, Zhonghua Sun, Conghui Xie, Hao Chen, Cunsheng Ding. 2024-04-29. Two classes of constacyclic codes with a square-root-like lower bound. https://arxiv.org/abs/2404.18438

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