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 $\mathrm{R}$.

翻译：本研究为获取更优编码，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。我们深入探讨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。作为应用实例，通过若干典型算例对所得结果进行了验证。此外，我们提出了一种新型生成矩阵的构造方法，从而获得了较现有文献参数更优的编码。最后，以列表形式展示了在该环$\mathrm{R}$上构造的块码。