计算机工程与科学 ›› 2021, Vol. 43 ›› Issue (01): 89-94.
• 计算机网络与信息安全 • 上一篇 下一篇
薛文芳，王维琼，李亚伟
收稿日期:
修回日期:
接受日期:
出版日期:
发布日期:
基金资助:
XUE Wen-fang,WANG Wei-qiong,LI Ya-wei
Received:
Revised:
Accepted:
Online:
Published:
摘要： 低重线性码在秘密共享方案、认证码、结合方案及强正则图的构造中有重要的应用。借助布尔函数构造出了一类二元三重或四重线性码，应用有限域上的特征和理论与布尔函数的Walsh谱确定了这类码的参数及重量分布。文中得到的三重码可用来构造秘密共享方案和结合方案，且所构造出的线性码的对偶码均为关于Sphere-packing界的最优码或几乎最优码。
关键词: 线性码, 重量分布, Weil和, 布尔函数, Walsh变换
Abstract: Linear codes with a few weights have important applications in secret sharing schemes, authentication codes, association schemes, and strong regular graphs. A class of 3-weight or 4-weight linear codes is provided with Boolean functions. The parameters and weight distributions of these codes are determined by the theory of character sums and the Walsh spectrum of Boolean functions. The proposed 3-weight codes can be used to construct secret sharing schemes and association schemes. The dual codes of the provided codes are optimal or almost optimal with respect to the sphere-packing bound.
Key words: linear code, weight distribution, Weil sum, boolean function, Walsh transform
薛文芳, 王维琼, 李亚伟. 一类三重或四重线性码的构造[J]. 计算机工程与科学, 2021, 43(01): 89-94.
XUE Wen-fang, WANG Wei-qiong, LI Ya-wei. Construction of a class of linear codes with three or four weights[J]. Computer Engineering & Science, 2021, 43(01): 89-94.
0 / / 推荐
导出引用管理器 EndNote|Ris|BibTeX
链接本文: http://joces.nudt.edu.cn/CN/
http://joces.nudt.edu.cn/CN/Y2021/V43/I01/89
