On $Z_{p^r}Z_{p^r}Z_{p^s}$-Additive Cyclic Codes

Abstract

In this paper, we introduce Z p r Z p r Z p s -additive cyclic codes for r ≤ s. These codes can be identified asWe determine the generator polynomials and minimal generating sets for this family of codes. Some previous works has been done for the case p = 2 with r = s = 1, r = s = 2, and r = 1, s = 2. However, we show that in these previous works the classification of these codes were incomplete and the statements in this paper complete such classification. We also discuss the structure of separable Z p r Z p r Z p s -additive cyclic codes and determine their generator polynomials. Further, we also study the duality of Z p s [x]-submodules. As applications, we present some examples and construct some optimal binary codes.