Constacyclic and Negacyclic Codes over $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ and their Equivalents over $mathbb{F}_{2}$
| dc.contributor.author | Mustafa ÖZKAN | |
| dc.contributor.author | Berk YENİCE | |
| dc.contributor.author | Ayşe Tuğba GÜROĞLU | |
| dc.date.accessioned | 2024-07-24T09:10:59Z | |
| dc.date.available | 2024-07-24T09:10:59Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | In 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. | |
| dc.identifier.DOI-ID | 10.33401/fujma.1124502 | |
| dc.identifier.uri | http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/23333 | |
| dc.language.iso | eng | |
| dc.title | Constacyclic and Negacyclic Codes over $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ and their Equivalents over $mathbb{F}_{2}$ | |
| dc.type | Araştırma Makalesi |