@article{article_1124502, title={Constacyclic and Negacyclic Codes over $\mathbb{F}_{2}+u\mathbb{F}_{2}+v\mathbb{F}_{2}$ and their Equivalents over $\mathbb{F}_{2}$}, journal={Fundamental Journal of Mathematics and Applications}, volume={5}, pages={228–233}, year={2022}, DOI={10.33401/fujma.1124502}, author={Özkan, Mustafa and Yenice, Berk and Güroğlu, Ayşe Tuğba}, keywords={Constacyclic code, Codes over rings, Negacyclic code}, abstract={<div style="text-align:justify;">In this work, we consider the finite ring $\mathbb{F}_{2}+u\mathbb{F}_{2}+v\mathbb{F}_{2}$, $u^{2}=1, v^{2}=0$, $u\cdot v=v\cdot u=0$ which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes in $\mathbb{F}_{2}+u\mathbb{F}_{2}+v\mathbb{F}_{2}$ with odd length. These codes are compared with codes that had priorly been obtained on the finite field $\mathbb{F}_{2}$. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over $\mathbb{F}_{2}+u\mathbb{F}_{2}+v\mathbb{F}_{2}$ with odd length $n$ is a quasicyclic code of index $4$ with length $4n$ in $\mathbb{F}_{2}$. In particular, the Gray images are applied to two different rings $S_{1}=\mathbb{F}_{2}+v\mathbb{F}_{2}$, $v^{2}=0$ and $S_{2}=\mathbb{F}_{2}+u\mathbb{F}_{2}$, $u^{2}=1$ and negacyclic and constacyclic images of these rings are also discussed. <br /> </div>}, number={4}, publisher={Fuat USTA}