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.
Categories: cs.IT math.IT math.RA