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arXiv · 1712.07783

Skew cyclic codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$

Reza Dastbasteh·Seyyed Hamed Mousavi·Taher Abualrub·Nuh Aydin·Javad Haghighat
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Abstract

In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta ]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an encoding and decoding algorithm is presented for skew cyclic codes over the ring $R$. Finally, based on the theory we developed in this paper, we provide examples of codes with good parameters over $F_{p}$ with different odd prime $p.$ In fact, example 25 in our paper is a new ternary code in the class of quasi-twisted codes. The other examples we provided are examples of optimal codes.

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Reza Dastbasteh, Seyyed Hamed Mousavi, Taher Abualrub, Nuh Aydin, Javad Haghighat. 2017-12-21. Skew cyclic codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$. https://arxiv.org/abs/1712.07783

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