Construction of skew cyclic codes over \(\mathbb F_q+v\mathbb F_q\). (English) Zbl 1300.94121
Summary: In this paper skew cyclic codes over the the family of rings \(\mathbb{F}_q+v\mathbb{F}_q\) with \(v^2=v\) are studied for the first time in its generality. Structural properties of skew cyclic codes over \(\mathbb{F}_q+v\mathbb{F}_q\) are investigated through a decomposition theorem. It is shown that skew cyclic codes over this ring are principally generated. The idempotent generators of skew-cyclic codes over \(\mathbb{F}_q\) and \(\mathbb{F}_q+v\mathbb{F}_q\) have been considered for the first time in literature. Moreover, a BCH type bound is presented for the parameters of these codes.
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