Skew cyclic codes over $\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p$
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1627-1638
https://doi.org/10.4134/BKMS.b160535
Published online November 30, 2018
Hamed Mousavi, Ahmad Moussavi, Saeed Rahimi
Tarbiat Modares University, Tarbiat Modares University, Emam Hossein University
Abstract : In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring $\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p$, where $p$ is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring $(\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p)[x;\theta]$ where $v^3=1$ and $\theta$ is an $\mathbb{F}_p$-automorphism such that $\theta(v)=v^2$. We show that when $n$ is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.
Keywords : skew cyclic coding, skew polynomial rings, Hamming distance, quasi cyclic coding
MSC numbers : Primary 11T71, 16S36, 68P30
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