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arXiv · 1910.06830

Reversible cyclic codes over $\mathbb{F}_q + u \mathbb{F}_q$

Om Prakash·Shikha Patel·Shikha Yadav
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Abstract

Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic codes of arbitrary length over the ring $ R = \mathbb{F}_q + u \mathbb{F}_q$, where $u^2=0 mod q$. First, we find a unique set of generators for cyclic codes over $R$, followed by a classification of reversible cyclic codes with respect to their generators. Also, under certain conditions, it is shown that dual of reversible cyclic code is reversible over $\mathbb{Z}_2+u\mathbb{Z}_2$. Further, to show the importance of these results, some examples of reversible cyclic codes are provided.

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Om Prakash, Shikha Patel, Shikha Yadav. 2019-10-15. Reversible cyclic codes over $\mathbb{F}_q + u \mathbb{F}_q$. https://arxiv.org/abs/1910.06830

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