Skew-constacyclic codes over $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$

In this paper, the investigation on the algebraic structure of the ring $\frac{\mathbb{F}q[v]}{\langle\,v^{q-v\,\rangle}$} and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over this ring. We explore the algebraic structure of skew-constacyclic codes, by using a linear Gray map and we determine their generator polynomials. Necessary and sufficient conditions for the existence of self-dual skew cyclic and self-dual skew negacyclic codes over $\frac{\mathbb{F}q[v]}{\langle\,v^{q-v\,\rangle}$} are given.