由特殊结构产生的二元LCD码以及自正交码  

Binary LCD Codes and Self-Orthogonal Code Generated by Special Structures

作　　者：陈行 唐春明[1] Chen Hang;Tang Chunming(College of Mathematics and Information,China West Normal University,Nanchong 637002,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《洛阳师范学院学报》2020年第8期5-8,共4页Journal of Luoyang Normal University

基　　金：大学生创新创业训练计划创新训练项目(cxcy2018203)。

摘　　要：线性码拥有理想的代数结构,在生活中有重要应用,因此怎样构造线性码成为了热门话题.文中主要构造了线性补对偶码(LCD)以及自正交码,在密码学中,LCD码常常用来对抗侧通道攻击等等.本文使用了一个特殊的集合产生了二元线性码,然后给出线性码是LCD码和自正交码的条件.除此之外,利用Krawtchouck多项式给出构造出的码的重量公式.Linear codes,which have an ideal algebraic structure,are of great importance for its application in life.Therefore,the construction of linear codes has become a hot topic.This paper mainly constructs linear complementary dual codes(LCD)which are often used to resist side channel attacks in cryptography and self-orthogonal codes.In this research,a special set is used to generate binary linear codes,and then the condition is given that the linear codes are LCD codes and self-orthogonal code.In addition,the Krawtchouck polynomial is used to give the weight formula of the constructed code.

关 键 词：线性码 LCD码 重量分布 自正交码 Krawtchouck多项式 

分 类 号：O29[理学—应用数学]