  In this paper we give the enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields when $(n,|\theta|)=1$ and for some cases when $(n,|\theta|)>1,$ where $n$ is the length of the code and $|\theta|$ is the order of automorphism $\theta.$ 
A Note on The Enumeration of Euclidean Self-Dual Skew-Cyclic Codes over   Finite Fields