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

QIAN Yi; LI Ping; TANG Yong-sheng

doi:10.3969/j.issn.0372-2112.2020.03.022

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

更新时间：2025-07-16

- A Construction Method of Quaternary Hermitian LCD Codes and Hermitian Self-Orthogonal Codes
- Acta Electronica Sinica Vol. 48, Issue 3, Pages: 577-581(2020)
- 作者机构：
  
  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
  3. 合肥工业大学数学学院,安徽,合肥,230009
  4. 合肥师范学院数学与统计学院,安徽,合肥,230601
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61572186, No.61972126, No.61572168);Fundamental Research Funds for the Central Universities (No.PA2019GDZC0097);Fundamental Project of Natural Science Foundation of Anhui Province (No.1808085MA15);Provincial Key Project of Natural Science of Higher Education Institute of Department of Anhui Province (No.KJ2018A0497)
- DOI：10.3969/j.issn.0372-2112.2020.03.022
  CLC： TN911.22
- Published Online：25 March 2020，
  
  Published：2020
- 稿件说明：
移动端阅览
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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2020.03.022.

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.

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.

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