On skew cyclic codes over $F_q+vF_q+v^2F_q$

Mohammad Ashraf; Ghulam Mohammad

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arXiv · 1504.04326

On skew cyclic codes over $F_q+vF_q+v^2F_q$

Mohammad Ashraf·Ghulam Mohammad

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Abstract

In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ over $F_{q}+vF_{q}+v^2F_{q}$ is a skew $3$-quasi cyclic code of length $3n$ over $F_{q}$. Further, it is shown that the skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ are principally generated. Finally, the idempotent generators of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ are also obtained.

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Mohammad Ashraf, Ghulam Mohammad. 2015-04-16. On skew cyclic codes over $F_q+vF_q+v^2F_q$. https://arxiv.org/abs/1504.04326

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