SKEW CYCLIC CODES OVER 𝔽p + v𝔽p + v2𝔽p

• Mousavi, Hamed (Department of Mathematics Tarbiat Modares University) ;
• Moussavi, Ahmad (Department of Mathematics Tarbiat Modares University) ;
• Rahimi, Saeed (Department of Information Technology Emam Hossein University)
• Received : 2015.06.25
• Accepted : 2018.02.01
• Published : 2018.11.30

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.

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