  Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta
: \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. 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
$\Phi_{\alpha,\theta}:\mathbb{F}_q^n\to\mathbb{F}_q^n$, defined by
$\Phi_{\alpha,\theta}(a_0,...,a_{n-2}, a_{n-1}):=(\alpha
\theta(a_{n-1}),\theta(a_0),...,\theta(a_{n-2}))$ for some
$\alpha\in\mathbb{F}_q\setminus\{0\}$ 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.
