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

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

paper

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

arXiv:2404.18438

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.