Quaternary Codes and Their Binary Images

被引：3

作者：

Wu, Yansheng ^{[1
]}

Li, Chao ^{[1
]}

Zhang, Lin ^{[1
]}

Xiao, Fu ^{[1
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Sch Comp Sci, Nanjing 210023, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2024年 / 70卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Codes; Linear codes; Codecs; Cryptography; Telecommunications; Computer science; Hamming weight; Quaternary code; simplicial complex; gray map; binary nonlinear code; minimal code; secret sharing scheme; LINEAR CODES;

D O I：

10.1109/TIT.2024.3358332

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun et al. Building upon their research, in this paper more linear codes over the ring Z(4) are constructed by simplicial complexes. Specifically, the Lee weight distributions of the resulting quaternary codes are determined and two infinite families of four-Lee-weight quaternary codes are obtained. Compared to the databases of Z(4 )codes by Aydin et al., at least nine new quaternary codes are found. Thanks to the special structure of the defining sets, we have the ability to determine whether the Gray images of certain obtained quaternary codes are linear or not. This allows us to obtain two infinite families of binary nonlinear codes and one infinite family of binary minimal linear codes. Furthermore, utilizing these minimal binary codes, some secret sharing schemes as a byproduct also are established.

引用

页码：4759 / 4768

页数：10

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