On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$

preprint2012arXivOpen access

In this paper, we study cyclic codes over the ring $\Z_p + u\Z_p +...+ u^{k-1}\Z_p$ , where $u^k =0$ . We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.

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On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$

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On cyclic codes over the ring Zp+uZp+...+uk−1ZpZ_p + uZ_p + ... + u^{k-1}Z_pZp​+uZp​+...+uk−1Zp​

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On cyclic codes over the ring $Z_p + uZ_p + ... + u^{k-1}Z_p$