On a characterization of certain maximal curves

For a -maximal curve of genus (q/n−1)q/2, where q/n is a nongap at some point, we show that is -isomorphic to the nonsingular model of a curve given by P(y)=A(x), where P is an additive separable polynomial of degree q/n and where A is a polynomial of degree q+1, under the further hypothesis that a certain field extension is Galois. In the particular case we were able to characterize such maximal curves without the assumption that a certain extension is Galois.