一类三元极小线性码的构造  

Construction of a Class of Ternary Minimal Linear Codes

作　　者：王玉琦 孙敏 陈文兵 WANG Yuqi;SUN Min;CHEN Wenbing(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2024年第2期20-25,共6页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11626032);安徽省高校优秀青年人才支持计划项目(gxyqZD2021120)。

摘　　要：极小线性码作为一类特殊的线性码,在秘密共享方案、安全多方计算等方面有着重要应用,因此构造有限域上极小线性码有着重要意义。本文基于指数和、Krawtchouk多项式和F3m中定义在特殊向量集上的函数,构造了一类新的不满足Ashikhmin-Barg条件的三元极小线性码,并确定了它们的重量分布和完全重量计数。Minimal linear codes,as a special category of linear codes,are critically important in applications such as secret sharing schemes and secure multi-party computation.It is of great significance to construct minimal linear codes over finite fields.Based on exponential sum,Krawtchouk polynomials and functions defined on special vector sets,we construct a new class of ternary minimal linear codes that do not satisfy the Ashikhmin-Barg condition,and then determine their weight distribution and complete weight enumerator.

关 键 词：线性码 极小码 汉明重量 完全重量计数 

分 类 号：O157.4[理学—数学]