Several Classes of Two-weight or Three-weight Linear Codes and Their Applications  

几类二重或三重线性码及其应用

作　　者：Shen Hongyan Liu Haibo 沈红艳;刘海波(成都信息工程大学应用数学学院,成都610066)

机构地区：[1]School of Applied Mathematics,Chengdu University of Information Technology,Chengdu 610066,China

出　　处：《数学理论与应用》2024年第3期25-49,共25页Mathematical Theory and Applications

基　　金：supported by the Natural Science Foundation of China (No.11901062);the Sichuan Natural Science Foundation (No.2024NSFSC0417)。

摘　　要：Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].近年来,少重量线性码因其在密钥共享方案、常组合码、强正则图中的应用,而被广泛研究.本文通过选取适当的定义集,基于Weil和构造几类二重或三重线性码,确定它们的重量分布和完全重量分布,并证明这些码是极小码.通过截断这些线性码得到两类射影二重码,并给出其对应的强正则图参数.本文推广了文献[7]的结果.

关 键 词：Weil sum Linear code Complete weight enumerator Minimal code Strongly regular graph 

分 类 号：O157.4[理学—数学]