Quaternary Codes and Their Binary Images

作者：Yansheng Wu, Chao Li, Lin Zhang, Fu Xiao · 发表于：IEEE Transactions on Information Theory · 年份：2024 · DOI：10.1109/tit.2024.3358332 · 被引用次数：7 · 研究领域：Coding theory and cryptography、Cooperative Communication and Network Coding、graph theory and CDMA systems

Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyunet al. Building upon their research, in this paper more linear codes over the ring Z4are 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 Z4codes by Aydinet 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.