Three Classes of Minimal Linear Codes Over the Finite Fields of Odd Characteristic

Abstract

Minimal linear codes are a special subclass of linear codes and have significant applications in secret sharing and secure two-party computation. In this paper, we focus on constructing minimal linear codes with $\frac {w_{\min }}{w_{\max }}\leq \frac {p-1}{p}$ for any odd prime $p$ based on a generic construction of linear codes, where $w_{\min }$ and $w_{\max }$ denote the minimum and maximum nonzero weights in a code, respectively. First, we present two new infinite families of minimal linear codes with two or three weights by selecting suitable subcode of linear codes which are not minimal. Second, we also present an infinite family of minimal linear codes by employing partial spreads, which can be viewed as a generalization of the construction of Ding et al. In addition, we determine the weight distributions of all these minimal linear codes.