Linear Codes over Finite Chain Rings

Abstract

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