Constacyclic and Negacyclic Codes over $mathbb{F}_{2}+umathbb{F}_{2}+vmathbb{F}_{2}$ and their Equivalents over $mathbb{F}_{2}$
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Tarih
2022
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Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
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Kaynak
Fundamental journal of mathematics and applications (Online)
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Cilt
5
Sayı
4
