The linear codes of t-designs held in the Reed-Muller and Simplex codes

被引：9

作者：

Ding, Cunsheng ^{[1
]}

Tang, Chunming ^{[2
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Clear Water Bay, Hong Kong, Peoples R China

[2] China West Normal Univ, Sch Math & Informat, Nanchong 637002, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2021年 / 13卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Cyclc code; Linear code; Reed-Muller code; t-design;

D O I：

10.1007/s12095-021-00470-6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A fascinating topic of combinatorics is the study of t-designs, which has a very long history. The incidence matrix of a t-design generates a linear code over GF(q) for any prime power q, which is called the linear code of the t-design over GF(q). On the other hand, some linear codes hold t-designs with t >= 1. The purpose of this paper is to study the linear codes of t-designs held in the Reed-Muller and Simplex codes. Some general theory for the linear codes of t-designs held in linear codes is presented. Several open problems are also presented.

引用

页码：927 / 949

页数：23