Two Infinite Families of Quaternary Codes

Abstract

Recently, Hyun et al. have utilized simplicial complexes to construct several infinite families of binary minimal and optimal linear codes. Building upon their work, we draw inspiration and extend their research by constructing codes over the ring $\mathbb {Z}_{4}$ with the aid of simplicial complexes. In this paper, we present two infinite families of quaternary codes, one of which is linear while the other is nonlinear. We analyze the Lee weight distributions of the resulting quaternary codes and compare them with the existing database of $\mathbb {Z}_{4}$ codes. Our findings reveal the discovery of several new quaternary codes. Furthermore, we also provide two classes of binary codes that can be obtained from these quaternary codes using the Gray map.