电子学报 ›› 2020, Vol. 48 ›› Issue (2): 296-302.DOI: 10.3969/j.issn.0372-2112.2020.02.011

• 学术论文 • 上一篇    下一篇

有限非链环上的自对偶常循环码及其应用

高健, 王永康   

  1. 山东理工大学数学与统计学院, 山东淄博 255000
  • 收稿日期:2018-07-21 修回日期:2019-03-28 出版日期:2020-02-25 发布日期:2020-02-25
  • 作者简介:高健 男,1987年生于山东德州.博士、硕士生导师,研究方向为编码理论及其应用.E-mail:dezhougaojian@163.com;王永康 男,1993年生于山东潍坊.硕士研究生,研究方向为编码理论及其应用.E-mail:zcyongkang@163.com
  • 基金资助:
    国家自然科学基金(No.11701336,No.11626144,No.11671235)

Self-Dual Constacyclic Codes over Finite Non-Chain Rings and Their Applications

GAO Jian, WANG Yong-kang   

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000, China
  • Received:2018-07-21 Revised:2019-03-28 Online:2020-02-25 Published:2020-02-25

摘要: 纠错码是提高信息传输效率与可靠性的重要手段.构造性能良好的线性码类是纠错码研究中的一个基本问题.本文主要讨论了有限非链环Fq[v]/(vmv)上自对偶常循环码的代数结构,包括Euclidean自对偶常循环码、Hermitian自对偶常循环码以及Hermitian自对偶常循环码的极大距离可分(MDS)码.本文给出了环Fq[v]/(vmv)上常循环码是Euclidean自对偶码的充分条件,以及是Hermitian自对偶码的充要条件,并利用Gray映射构造了有限域Fq上一些参数较好的自对偶码.特别地,本文得到了有限域F192上一个新的参数为[16,8,6]的Hermitian自对偶码.

关键词: 纠错码, 自对偶常循环码, Gray映射, 新的Hermitian自对偶码

Abstract: Error-correcting codes are important for the improvement of efficiency and security in information transmission.Constructing codes with good parameters is a fundamental problem in error-correcting codes.In this paper, we mainly study self-dual constacyclic codes over the finite nonchain ring Fq[v]/(vmv), including Euclidean self-dual constacyclic codes, Hermitian self-dual constacyclic codes and maximal distance separable (MDS) codes of Hermitian self-dual constacyclic codes.We give a necessary condition for constacyclic codes to be Euclidean self-dual and give a necessary and sufficient condition for constacyclic codes to be Hermitian self-dual over the ring Fq[v]/(vmv).Further, some good self-dual codes are constructed by the Gray map.Especially, a Hermitian self-dual code over F192 with parameters [16, 8, 6] is constructed.

Key words: error-correcting codes, self-dual constacyclic codes, gray map, new Hermitian self-dual codes

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