Abstract

Let be a finite commutative ring for a prime and any positive integers and . In this paper, we derive the explicit representation of cyclic codes over the ring of length , where and are coprime. We also discuss the dual of such cyclic codes over the ring and give a sufficient condition for the codes to be self-dual. Moreover, we study quasi-cyclic codes of length and index over the ring , and obtain some good codes satisfying the bound given in Dougherty and Shiromoto (2000) over the ring as an example.