In this study, we introduce \(\mathbb {F}_2\) \(\mathbb {F}_4\) -skew cyclic codes as a generalization of skew cyclic codes over \(\mathbb {F}_4\) . We characterize algebraic structures of \(\mathbb {F}_2\) \(\mathbb {F}_4\) -skew cyclic codes by determining their generating polynomials and minimal spanning sets. We also exhibit generator matrices for these codes. Furthermore, we examine the duals of \(\mathbb {F}_2\) \(\mathbb {F}_4\) -skew cyclic codes concerning a certain inner product and identify their generating polynomials. Finally, as an application of \(\mathbb {F}_2\) \(\mathbb {F}_4\) -skew cyclic codes, we present some examples of near-MDS codes over \(\mathbb {F}_4\) and optimal binary linear codes which are Gray images of \(\mathbb {F}_2\) \(\mathbb {F}_4\) -skew cyclic codes.
