两类三元极小码与其完全重量计数器  

Two Classes of Minimal Ternary Linear Codes and Their Complete Weight Enumerators

作　　者：刘海波 廖群英 朱灿泽 LIU Haibo;LIAO Qunying;ZHU Canze(School of Applied Mathematics,Chengdu University of Information Technology,Chengdu,Sichuan,610225,P.R.China;School of Mathematical Sciences,Sichuan Normal University,Chengdu,Sichuan,610066,P.R.China)

机构地区：[1]成都信息工程大学应用数学学院,四川成都610225 [2]四川师范大学数学科学学院,四川成都610066

出　　处：《数学进展》2024年第2期390-406,共17页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11901062);supported by NSFC(No.12071321)。

摘　　要：最近,极小码因其在秘钥共享和二方计算中的应用被广泛研究.构造反Ashikhmin-Barg界的极小码,然后确定其完全重量计数器是编码与密码中有趣的研究.本文基于指数和与Krawtchouk多项式,利用定义在F_(3)^(m)中的向量集函数给出了两类反Ashikhmin-Barg三元极小码,并确定了其完全重量计数器.Recently,minimal linear codes have been extensively studied due to their applications in secret sharing schemes and two-party computations.Constructing minimal linear codes violating the Ashikhmin–Barg condition and then determining their weight distributions are interesting in coding theory and cryptography.In this paper,based on exponential sums,Krawtchouk polynomials and a function defined on special sets of vectors in F_(3)^(m),two new classes of minimal ternary linear codes violating the Ashikhmin–Barg condition are presented,and then their complete weight enumerators are determined.

关 键 词：线性码 极小码 极小向量 重量分布 完全重量计数器 

分 类 号：O157.4[理学—数学]