Skew cyclic codes over 𝔽qR

In this paper, we study the algebraic structure of [Formula: see text]-skew cyclic codes, where [Formula: see text] denotes the ring [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We determine generator polynomials for [Formula: see text]-skew cyclic codes and generator idempotents for separable codes. We also give conditions for the dual of a [Formula: see text]-skew cyclic code to be another [Formula: see text]-skew cyclic code. We introduce a Gray map from [Formula: see text] to [Formula: see text] where [Formula: see text] and [Formula: see text] are non-negative integers. As an application, we construct quantum codes from these codes.