Double skew cyclic codes over ${\mathbb{F}}_q+v{\mathbb{F}}_q$

Abstract

In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}={\mathbb{F}}_q+v{\mathbb{F}}_q,v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets, generator matrices, and the dual codes over the ring $\mathrm{R}$. As an implementation, the obtained results are illustrated with some good examples. Moreover, we introduce a construction for new generator matrices and thus achieve codes with improved parameters compared to those found in existing literature. Finally, we tabulate our obtained block codes over the ring $\mathrm{R}$.

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