Abstract
Let R be a Galois ring, GR(p(n),r), of characteristic p(n) and of order p(nr). In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N, in terms of that of length, p(s), where s = v(p)(N) and v(p) are the p-adic valuation. As a result, Hamming distance and dual codes are obtained. In addition, we compute the exact number of distinct cyclic codes over R when n = 2.