A generalization of the Giulietti–Korchmáros maximal curve

We introduce a family of algebraic curves over F(q)(2n) ( for an odd n) and show that they are maximal. When n = 3, our curve coincides with the F(q)(6)-maximal curve that has been found by Giulietti and Korchmaros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to be covered by the Hermitian curve.