On skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$
Mohammad Ashraf$^{1}$ and Ghulam Mohammad$^{2}$
In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$
and $p$ is an odd prime. The structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ have
been studied by using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$,
it has been proved that the Gray image of a skew cyclic code of length $n$ over $F_{q}+vF_{q}+v^2F_{q}$ is a
skew $3$quasi cyclic code of length $3n$ over $F_{q}$. Further, it is shown that the skew cyclic codes over
$F_{q}+vF_{q}+v^2F_{q}$ are principally generated. Finally, the idempotent generators of skew cyclic codes over
$F_{q}+vF_{q}+v^2F_{q}$ have also been studied.
Tbilisi Mathematical Journal, Vol. 11(2) (2018), pp. 3545
