Linear codes over finite chain rings

Abstract

In this paper, we study linear codes over finite chain rings. We relate linear cyclic codes, (1 + γk)-cyclic codes and (1 γk)-cyclic codes over a finite chain ring R, where γ is a fixed generator of the unique maximal ideal of the finite chain ring R, and the nilpotency index of γ is k+1. We also characterize the structure of (1+γk)-cyclic codes and (1 - γk)-cyclic codes over finite chain rings.