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.
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页码：407 / 423
页数：17
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