On cyclic codes over F_{p^k} + vF_{p^k} + v^2 F_{p^k} + ... + v^k F_{p^k}

Abstract

In this paper, we investigate cyclic code over the ring F_p^k + vF_p^k + v²F_p^k + ... + v^rF_p^k, where v^r+1 = v, p a prime number, r > 1 and gcd(r,p) = 1, we prove as generalisation of [10] that these codes are principally generated, give generator polynomial and idempotent depending on idempotents over this ring as response to an open problem related in [12]. we also give a gray map and proprieties of the related dual code.