Özkan, MustafaYenice, BerkGüroğlu, Ayşe Tuğba2024-06-122024-06-1220222645-8845https://doi.org/10.33401/fujma.1124502https://search.trdizin.gov.tr/yayin/detay/1147494https://hdl.handle.net/20.500.14551/13272In this work, we consider the finite ring $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$, $u^{2}=1, v^{2}=0$, $ucdot v=vcdot u=0$ which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes in $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ 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 $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ 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 $S_{1}=mathbb{F}_{2}+vmathbb{F}_{2}$, $v^{2}=0$ and $S_{2}=mathbb{F}_{2}+umathbb{F}_{2}$, $u^{2}=1$ and negacyclic and constacyclic images of these rings are also discussed.en10.33401/fujma.1124502info:eu-repo/semantics/openAccessArticle542282331147494