奇特征域上一类二重量线性码  

A class of two-weight linear codes over finite fields of odd characteristic

作　　者：段冰冰 韩广国[1] 亓延峰[1] DUAN Bing-bing;HAN Guang-guo;QI Yan-feng(School of Science,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《高校应用数学学报（A辑）》2023年第3期364-372,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：浙江省自然科学基金(LY18A010012,LY21A010013)。

摘　　要：线性码在通信,数据存储和秘密共享方案等领域都有很好的应用.基于定义集的构造方法,选择二变量函数确定有限域上的定义集,从而构造了奇特征域上一类二重量线性码,并利用加法特征,乘法特征以及高斯和等确定了线性码的具体参数和重量分布.此外,大部分线性码是极小码,这些码可用于构造秘密共享方案.Linear codes have applications in communication,data storage systems and secret sharing schemes.A class of two weight linear codes is obtained by the defining sets determined by the bivariate functions over finite fields of odd characteristic.The parameters and weight distributions of linear codes are determined by the additive characters,multiplicative characters and Gauss sums.Additionally,most of linear codes are minimal and thus they are suitable for secret sharing schemes.

关 键 词：线性码 重量分布 加法特征 乘法特征 高斯和 

分 类 号：O157.04[理学—数学]