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
收藏
页码：927 / 949
页数：23
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