@article{article_763109, title={Linear Codes Over the Ring $Z_8+uZ_8+vZ_8$}, journal={Conference Proceedings of Science and Technology}, volume={3}, pages={19–23}, year={2020}, author={Çalışkan, Basri}, keywords={Duality, Generator matrix, Lee weight, Linear codes over rings}, abstract={<div style="text-align:justify;"> <span style="font-size:14px;">In this paper, we introduce the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ where $u^{2}=u$, $v^{2}=v$, $uv=vu=0$ over which the linear codes are studied. it’s shown that the ring $R=\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ is a commutative, characteristic 8 ring with $u^{2}=u$, $v^{2}=v$, $uv=vu=0$. Also, the ideals of $\mathbb{Z}_{8}+u\mathbb{Z}_{8}+v\mathbb{Z}_{8}$ are found. Moreover, we define the Lee distance and the Lee weight of an element of $R$ and investigate the generator matrices of the linear code and its dual. </span> </div>}, number={1}, publisher={Murat TOSUN}