Separable Degree of the Gauss Map and Strict Dual Curves Over Finite Fields

Let X be a non-degenerate projective algebraic curve and denote by X similar to its strict dual curve. The map. : X -. X similar to is called (strict) Gauss map of 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.