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arXiv · 1504.07860

Skew cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$

Minjia Shi·Ting Yao·Adel Alahmadi·Patrick Solé
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Abstract

In this article, we study skew cyclic codes over ring $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and $v^{3}=v$. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over $R$ by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent generators of skew cyclic codes over $\mathbb{F}_{q}$ and $R$ are considered.

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Minjia Shi, Ting Yao, Adel Alahmadi, Patrick Solé. 2015-04-29. Skew cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$. https://doi.org/10.1587/transfun.e98.a.1845

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