A note on the duals of skew constacyclic codes

Let Fq be a finite field with q elements and denote by θ : Fq → Fq an automorphism of Fq. In this note, we deal with skew constacyclic codes, i.e. linear codes of Fnq which are invariant under the action of a semi-linear map T : Fnq → F n q , defined by T (a0, ..., an−2, an−1) := (αan−1, a0, ..., an−2) for some α ∈ Fq −{0} and n ≥ 2. In particular, we study some algebraic and geometric properties of their dual codes and we give some Magma Programs as applications of the main theoretical results.