A note on the duals of skew constacyclic codes

Let ${\mathbb{F}}_q$ be a finite field with $q$ elements and denote by $\theta : $\mathbb{F}$q\to$\mathbb{F}$q$anautomorphismof$$\mathbb{F}$q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of ${\mathbb{F}}_q^n$ which are invariant under the action of a semi-linear map ${\mathrm{\Phi }}_{\alpha ,\theta }:{\mathbb{F}}_q^n\to {\mathbb{F}}_q^n$, defined by $\Phi{\alpha,\theta}(a_0,…,a{n-2}, a{n-1}):=(\alpha \theta(a_{n-1}),\theta(a_0),…,\theta(a_{n-2}))$forsome$\alpha\in$\mathbb{F}$_q\setminus{0}$and$n\geq 2$. In particular, we study some algebraic and geometric properties of their dual codes and we give some consequences and research results on $1$-generator skew quasi-twisted codes and on MDS skew constacyclic codes.