一类三重循环码及其重量分布  

A Class of Three-Weight Cyclic Codes and Their Weight Distribution

作　　者：刘芳蕊 范翠玲 LIU Fang-rui;FAN Cui-ling(School of Mathematics,Southwest Jiaotong University,Chengdu Sichuan 610031,China)

机构地区：[1]西南交通大学数学学院,成都610031

出　　处：《西华师范大学学报（自然科学版）》2022年第3期276-282,共7页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11971395);四川科技计划基础项目(2018JY0261)。

摘　　要：循环码是线性码的一个子类,具有优异的编译码性能,因此在数据存储、通讯系统和信息安全等诸多领域有着重要的应用。本文提出了一类新型三重循环码,其对偶码有2个零因子,并基于指数和理论确定了这类循环码的重量分布。此外,本文还讨论了此类循环码在密钥共享中的应用。As a subclass of linear codes with efficient encoding and decoding algorithms,Cyclic codes have important applications in data storage systems,communication systems,information security and so on.This paper presents a class of new three-weight cyclic codes whose duals have two zeros.Moreover,the weight distribution of proposed cyclic codes is settled by the theory of exponential sums over finite fields.What s more,the application of the proposed cyclic codes to secret sharing is also discussed.

关 键 词：循环码 重量分布 指数和 密钥共享 

分 类 号：O157.4[理学—数学] O236.2[理学—基础数学]