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.

Keywords

• Linear codes
• one-Lee weight codes
• gray map
• optimal codes

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