Linear codes of 2-designs as subcodes of the generalized Reed-Muller codes

被引：1

作者：

He, Zhiwen ^{[1
]}

Wen, Jiejing ^{[2
,3
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China

[2] Shandong Univ, Key Lab Cryptol Technol & Informat Secur, Minist Educ, Qingdao 266237, Peoples R China

[3] Shandong Univ, Sch Cyber Sci & Technol, Qingdao 266237, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2021年 / 13卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Ternary code; 2-design; Incidence matrix; Generalized Reed-Muller code; INFINITE FAMILIES; 3-DESIGNS;

D O I：

10.1007/s12095-021-00472-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper is devoted to the affine-invariant ternary codes defined by Hermitian functions. We first compute the incidence matrices of the 2-designs supported by the minimum weight codewords of these ternary codes. Then we show that the linear codes spanned by the rows of these incidence matrices are subcodes of the 4-th order generalized Reed-Muller codes and also hold 2-designs. Finally, we determine the dimension and develop a lower bound on the minimum distance of the ternary linear codes.

引用

页码：407 / 423

页数：17

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