Let p be a prime and \(\mathbb {F}_q\) be the finite field of order \(q=p^m\) . In this paper, we study \(\mathbb {F}_q\mathcal {R}\) -skew cyclic codes where \(\mathcal {R}=\mathbb {F}_q+u\mathbb {F}_q\) with \(u^2=u\) . To characterize \(\mathbb {F}_q\mathcal {R}\) -skew cyclic codes, we first establish their algebraic structure and then consider a non-degenerate inner product to discuss the dual containing properties of these codes. Further, we define a Gray map over \(\mathbb {F}_q\mathcal {R}\) and obtain their \(\mathbb {F}_q\) -Gray images. As an application, we apply the CSS (Calderbank–Shor–Steane) construction on Gray images of dual containing \(\mathbb {F}_q\mathcal {R}\) -skew cyclic codes and obtain many quantum codes with better parameters than the best-known codes available in the literature.
