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Turkish Journal of Mathematics

DOI

10.3906/mat-1602-35

Abstract

In this paper, we study cyclic codes over the ring $R=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+u^{2}\mathbb{Z}_{4}$,where $u^{3}=0$. We investigate Galois extensions of this ring and the ideal structure of these extensions.The results are then used to obtain facts about cyclic codes over $R$. We also determine the general form of the generator of a cyclic code and find its minimal spanning sets. Finally, we obtain many new linear codes over $\mathbb{Z}_4$ by considering Gray images of cyclic codes over $R$.

First Page

1235

Last Page

1247

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Mathematics Commons

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