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

Reza Dastbasteh; Seyyed Hamed Mousavi; Taher Abualrub; Nuh Aydin; Javad Haghighat

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

Information Theory 2017-12-22 v1 math.IT

Authors: Reza Dastbasteh , Seyyed Hamed Mousavi , Taher Abualrub , Nuh Aydin , Javad Haghighat

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.

Keywords

coding theory maximum distance separable code sequence design

Cite

@article{arxiv.1712.07783,
  title  = {Skew cyclic codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$},
  author = {Reza Dastbasteh and Seyyed Hamed Mousavi and Taher Abualrub and Nuh Aydin and Javad Haghighat},
  journal= {arXiv preprint arXiv:1712.07783},
  year   = {2017}
}

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

Abstract

Keywords

Cite

Related papers