Skew Cyclic Codes over $mathbb{Z}_{8}+umathbb{Z}_{8}+vmathbb{Z}

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Turkish Journal of Mathematics and Computer Science
Volume:15 Issue:1
Skew Cyclic Codes over $mathbb{Z}_{8}+umathbb{Z}_{8}+vmathbb{Z}_{8}$

Skew Cyclic Codes over $mathbb{Z}_{8}+umathbb{Z}_{8}+vmathbb{Z}_{8}$

Authors : Basri ÇALIŞKAN, Kemal BALIKÇI

Pages : 96-103

Doi:10.47000/tjmcs.995569

View : 56 | Download : 18

Publication Date : 2023-06-30

Article Type : Research Paper

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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