一种三元线性互补对偶码与自正交码的构造方法  

A Construction Method of Ternary Linear Complementary Dual Codes and Self-orthogonal Codes

作　　者：李平[1] 张嘉媛 孙中华[1] LI Ping;ZHANG Jiayuan;SUN Zhonghua(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《电子与信息学报》2022年第11期4018-4024,共7页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(61972126,61572168,62002098)。

摘　　要：有限域上线性互补对偶(LCD)码有良好的相关特性和正交特性,并能够防御信道攻击。自正交码是编码理论中一类非常重要的码,可以用于构造量子纠错码。该文研究了有限域F3上的LCD码。通过选取4种合适的定义集,利用有限域F3上线性码是LCD码或自正交码的判定条件,构造了4类3元LCD码和一些自正交码,并研究了这4类线性码的对偶码,得到了一些3元最优线性码。Due to good correlation and orthogonal properties,Linear Complementary Dual(LCD)codes over the finite fields can be used to defend against channel attacks.As a very important class of codes in coding theory,self-orthogonal codes can be used to construct quantum error-correcting codes.In this paper,LCD codes over the finite field F3 are studied.By selecting appropriate defining sets and using the conditions for linear codes over the finite field F3 to be LCD codes or self-orthogonal codes,four kinds of ternary LCD codes and some self-orthogonal codes are constructed.And the dual codes of these four kinds of liner codes are also studied and some ternary optimal linear codes are obtained.

关 键 词：线性码 3元线性互补对偶码 自正交码 定义集 

分 类 号：TN911.22[电子电信—通信与信息系统]