Several families of [formula omitted]-ary minimal linear codes with [formula omitted

Abstract

Constructing minimal linear codes is an interesting research topic due to their applications in coding theory and cryptography. Ashikhmin and Barg pointed out that wmin∕wmax>(q−1)∕q is a sufficient condition for a linear code over the finite field Fq to be minimal, where wmin and wmax respectively denote the minimum and maximum nonzero weights in a code. However, only a few families of minimal linear codes over Fq with wmin∕wmax≤(q−1)∕q were reported in the literature. In this paper, we obtain several families of minimal q-ary linear codes with wmin∕wmax≤(q−1)∕q. The weight distributions of all the constructed minimal linear codes are presented.