Skew cyclic codes over $\mathbb{F}_p+v\mathbb{F}_p+v^2\mathbb{F}_p$
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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.
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.
참고문헌 (11)
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