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.

An important concept in secret sharing scheme is the access structure. However, determining the access structure of the secret sharing scheme based on a linear code is a very difficult problem. In this work, we provide a method to construct a class of two-weight linear codes over finite rings. Based on the two-weight codes, we present an access structure of a secret sharing scheme.