Two new families of linear codes with five Lee-weights over Fq+uFq and their Gray images

Abstract

Linear codes with few weights have many applications in secret sharing, strongly regular graphs and association schemes. In this paper, by taking proper defining sets, we first present two new infinite families of linear codes with five Lee-weights over $F_q+u{F}_q$ and exactly determine the complete weight enumerators of their Gray images. As an application, we also show that Gray images of the two families of linear codes are two new infinite families of minimal linear codes with $\frac{w_{\min }}{w_{\max }}<\frac{q-1}{q}$, where $w_{\min }$ and $w_{\max }$ denote the minimum and maximum nonzero weights in the code, respectively.