Separable degree of the Gauss map and strict dual curves over finite fields

Let $\mathcal{X}$ be a projective algebraic curve and denote by ${\mathcal{X}}^{{}^{\mathrm{\prime }}}$ its strict dual curve. The map $\gamma:$\mathcal{X}$ \longrightarrow $\mathcal{X}$^{'}$iscalled(strict)Gaussmapof$$\mathcal{X}$$. In this manuscript, we study the separable degree of the Gauss map of curves defined over finite fields. In particular, we give a generalization of a known result on the separable degree of the Gauss map of plane Frobenius nonclassical curves. We also obtain a characterization of certain plane strange curves.