| 一种四元厄米特LCD码与厄米特自正交码的构造方法 |
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| 引用本文： | 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. |
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| 作者姓名： | 钱毅 李平 唐永生 |
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| 作者单位： | 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 |
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| 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.
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| 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 |
| 收稿时间： | 2019-02-25 |
A Construction Method of Quaternary Hermitian LCD Codes and Hermitian Self-Orthogonal Codes |
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| 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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| Authors: | QIAN Yi LI Ping TANG Yong-sheng |
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| Affiliation: | 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 |
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| 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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| Keywords: | linear codes quaternary codes optimal codes Hermitian linear complementary dual(LCD) codes Hermitian self-orthogonal codes Hermitian dual codes |
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