一种四元厄米特LCD码与厄米特自正交码的构造方法

doi:10.3969/j.issn.0372-2112.2020.03.022

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

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. 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
- 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. 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/Abstract

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

中图分类号:

TN911.22

钱毅, 李平, 唐永生. 一种四元厄米特LCD码与厄米特自正交码的构造方法[J]. 电子学报, 2020, 48(3): 577-581.

QIAN Yi, LI Ping, TANG Yong-sheng. A Construction Method of Quaternary Hermitian LCD Codes and Hermitian Self-Orthogonal Codes[J]. Acta Electronica Sinica, 2020, 48(3): 577-581.

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一种四元厄米特LCD码与厄米特自正交码的构造方法

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

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