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

作　　者：钱毅 李平[1] 唐永生 QIAN Yi;LI Ping;TANG Yong-sheng(School of Mathematics,Hefei University of Technology,Hefei,Anhui 230009,China;School of Mathematics and Statistics,Hefei Normal University,Hefei,Anhui 230601,China)

机构地区：[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

出　　处：《电子学报》2020年第3期577-581,共5页Acta Electronica Sinica

基　　金：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)。

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.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.

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 

分 类 号：TN911.22[电子电信—通信与信息系统]