A class of constacyclic BCH codes of length n=q2m-12q2-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=\frac{q^{2m}-1}{2\left( q^2-1\right) }$$\end{document} and related quantum codesA class of constacyclic BCH codes...J. Zhang et al.

被引：0

作者：

Jiayuan Zhang ^{[1
]}

Xiaoshan Kai ^{[1
]}

Ping Li ^{[1
]}

Shixin Zhu ^{[1
]}

机构：

[1] Hefei University of Technology,School of Mathematics

来源：

Quantum Information Processing | / 23卷 / 12期

关键词：

BCH code; Cyclotomic coset; Hermitian construction; Quantum code;

D O I：

10.1007/s11128-024-04605-5

中图分类号：

学科分类号：

摘要：

In this paper, a class of narrow-sense constacyclic BCH codes over Fq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q^2}$$\end{document} with length n=q2m-12q2-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=\frac{q^{2m}-1}{2\left( q^2-1\right) }$$\end{document} is studied, where q≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q\ge 3$$\end{document} is an odd prime power and m≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m\ge 2$$\end{document} is even. The maximum designed distance such that narrow-sense constacyclic BCH codes over Fq2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q^2}$$\end{document} with length n containing their Hermitian dual codes is determined. We obtain some new quantum codes by using such narrow-sense constacyclic BCH codes. Our constructions not only have larger designed distance but also have better parameters than the ones in the literature.

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