On the Gray Image of Cyclic Codes over Finite Chain Rings

Abstract

We introduce (1-γ)-cyclic code and cyclic codes over the finite chain ring R. We prove that the Gray image of a linear (1-γ)-cyclic code over R of length n is a distance invariant quasi-cyclic code over Fpk. We also prove that if (n,p) = 1, then every code over Fpk which is the Gray image of a cyclic code over R of length n is equivalent to a quasi-cyclic code.