Constacyclic and Negacyclic Codes over $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ and their Equivalents over $mathbb{F}_{2}$
| dc.contributor.author | Özkan, Mustafa | |
| dc.contributor.author | Yenice, Berk | |
| dc.contributor.author | Güroğlu, Ayşe Tuğba | |
| dc.date.accessioned | 2024-06-12T10:05:10Z | |
| dc.date.available | 2024-06-12T10:05:10Z | |
| dc.date.issued | 2022 | |
| dc.department | Trakya Üniversitesi | en_US |
| 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. | en_US |
| dc.identifier.doi | 10.33401/fujma.1124502 | |
| dc.identifier.endpage | 233 | en_US |
| dc.identifier.issn | 2645-8845 | |
| dc.identifier.issue | 4 | en_US |
| dc.identifier.startpage | 228 | en_US |
| dc.identifier.trdizinid | 1147494 | en_US] |
| dc.identifier.uri | https://doi.org/10.33401/fujma.1124502 | |
| dc.identifier.uri | https://search.trdizin.gov.tr/yayin/detay/1147494 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14551/13272 | |
| dc.identifier.volume | 5 | en_US |
| dc.indekslendigikaynak | TR-Dizin | en_US |
| dc.language.iso | en | en_US |
| dc.relation.ispartof | Fundamental journal of mathematics and applications (Online) | en_US |
| dc.relation.publicationcategory | Makale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.title | Constacyclic and Negacyclic Codes over $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ and their Equivalents over $mathbb{F}_{2}$ | en_US |
| dc.type | Article | en_US |
