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- W765167617 abstract "In this paper, we study the linear codes over the commutative ring $R=F_{q}+vF_{q}+v^{2}F_{q}$ and their Gray images, where $v^{3}=v$. We define the Lee weight of the elements of $R$, we give a Gray map from $R^{n}$ to $F^{3n}_{q}$ and we give the relation between the dual and the Gray image of a code. This allows us to investigate the structure and properties of self-dual cyclic, formally self-dual and the Gray image of formally self-dual codes over $R$. Further, we give several constructions of formally self-dual codes over $R" @default.
- W765167617 created "2016-06-24" @default.
- W765167617 creator A5027852072 @default.
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- W765167617 date "2015-04-30" @default.
- W765167617 modified "2023-09-27" @default.
- W765167617 title "The Dual and the Gray Image of Codes over $mathbb{F}_{q}+vmathbb{F}_{q}+v^{2}mathbb{F}_{q}$" @default.
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