Skew Cyclic Codes over $\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$

Abstract

In this paper, we study the skew cyclic codes over the ring $S=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$, where $u^{2}=u$, $v^{2}=v$, $uv=vu=0$. We consider these codes as left $S[x,\theta]$-submodules and use the Gray map on $S$ to obtain the $\mathbb{Z}_{8}$-images. The generator and parity-check matrices of a free $\theta$-cyclic code of even length over $S$ are determined. Also, these codes are generalized to double skew-cyclic codes. We give some examples using Magma computational algebra system.

Keywords

• Double-cyclic codes
• Gray map
• linear codes
• skew-cyclic codes

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