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 better parameters than existing codes in the literature. Finally, we tabulate double skew cyclic codes of block length over the ring $\mathrm{R}$.

翻译：本文为获取更优编码，聚焦于环 $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$（其中 $q$ 为素数幂）上的双斜循环码。我们研究了该环上码的生成多项式、最小生成集、生成矩阵以及对偶码。作为具体实现，通过若干优秀算例对所得结果进行了说明。此外，我们提出了一种新型生成矩阵的构造方法，从而获得了比现有文献中参数更优的编码。最后，我们列出了环 $\mathrm{R}$ 上块长度参数的双斜循环码表格。