Abstract

Let be a finite field of cardinality , and be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over of length can be obtained from self-dual cyclic code over R of length and by a Gray map preserving orthogonality and distances from R onto .