- Turkish Journal of Mathematics and Computer Science
- Vol: 15 Issue: 1
- Skew Cyclic Codes over $\\mathbb{Z}_{8}+u\\mathbb{Z}_{8}+v\\mathbb{Z}_{8}$
Skew Cyclic Codes over $\\mathbb{Z}_{8}+u\\mathbb{Z}_{8}+v\\mathbb{Z}_{8}$
Authors : Basri ÇALIŞKAN, Kemal BALIKÇI
Pages : 96-103
Doi:10.47000/tjmcs.995569
View : 12 | Download : 11
Publication Date : 2023-06-30
Article Type : Research Article
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