电子学报 ›› 2020, Vol. 48 ›› Issue (3): 577-581.DOI: 10.3969/j.issn.0372-2112.2020.03.022

• 学术论文 • 上一篇    下一篇

一种四元厄米特LCD码与厄米特自正交码的构造方法

钱毅1, 李平1, 唐永生2   

  1. 1. 合肥工业大学数学学院, 安徽合肥 230009;
    2. 合肥师范学院数学与统计学院, 安徽合肥 230601
  • 收稿日期:2019-02-25 修回日期:2019-06-20 出版日期:2020-03-25 发布日期:2020-03-25
  • 作者简介:钱毅 男,1995年生,安徽铜陵人,合肥工业大学数学学院硕士研究生,研究方向为代数编码.E-mail:1304123894@qq.com;李平 男,1971年生,安徽无为人,合肥工业大学数学学院副教授,硕士生导师.研究方向为代数编码及非线性移位寄存器序列.E-mail:lpmath@126.com;唐永生 男,1981年生,安徽庐江人,合肥师范学院数学与统计学院副教授.研究方向为代数编码、量子信息以及线性和非线性移位寄存器序列.E-mail:ysh_tang@163.com
  • 基金资助:
    国家自然科学基金(No.61572186,No.61972126,No.61572168);中央高校基本科研业务费专项资金项目(No.PA2019GDZC0097);安徽省自然科学基金面上项目(No.1808085MA15);安徽省教育厅高校省级自然科学重点项目(No.KJ2018A0497)

A Construction Method of Quaternary Hermitian LCD Codes and Hermitian Self-Orthogonal Codes

QIAN Yi1, LI Ping1, TANG Yong-sheng2   

  1. 1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
    2. School of Mathematics and Statistics, Hefei Normal University, Hefei, Anhui 230601, China
  • Received:2019-02-25 Revised:2019-06-20 Online:2020-03-25 Published:2020-03-25

摘要: 有限域上线性互补对偶(LCD)码具有良好的结构和性质,并在双用户加法器信道中得到了广泛的应用.自正交码是编码理论中一类重要的线性码,常被用于构造量子纠错码.本文根据有限域上线性码是厄米特LCD码或厄米特自正交码的判定条件,通过选取合适的定义集,构造出了四类四元厄米特LCD码和厄米特自正交码.同时,本文还研究了这四类线性码的厄米特对偶码,并得到了一些四元最优线性码.

关键词: 线性码, 四元码, 最优码, 厄米特LCD码, 厄米特自正交码, 厄米特对偶码

Abstract: Linear complementary dual (LCD) codes over finite fields have good structure and properties,and are widely used in two-user adder channels.Self-orthogonal codes are important linear codes in coding theory and are often used to construct quantum error-correcting codes.In this paper,we consider that linear codes over finite fields are Hermitian LCD codes or Hermitian self-orthogonal codes.By selecting the appropriate set of definitions,four kinds of quaternary Hermitian LCD codes and Hermitian self-orthogonal codes are constructed.At the same time,Hermitian dual codes of these four kinds of linear codes are studied and some quaternary optimal linear codes are obtained.

Key words: linear codes, quaternary codes, optimal codes, Hermitian linear complementary dual(LCD) codes, Hermitian self-orthogonal codes, Hermitian dual codes

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