One Weight Codes Over the Ring $F_q[v]/(v^s-1)$

Abstract

In this study, we obtain one-Lee weight codes over a class of nonchain rings and study their structures.
 We give an explicit construction for one-Lee weight codes. A method to derive more one-Lee weight codes from given a one-Lee weight code is also represented. By defining and making use of a distance-preserving Gray map, we get a family of optimal one-Hamming weight codes over finite fields.