A new family of maximal curves

In this article we construct for any prime power q and odd n ≥ 5, a new F_q2n -maximal curve Xn. Like the Garcia–G¨uneri–Stichtenoth maximal curves, our curves generalize the Giulietti–Korchmaros maximal curve, though in a different way. We compute the full automorphism group of X_n, yielding that it has precisely q(q² − 1)(qⁿ + 1) automorphisms. Further, we show that unless q = 2, the curve X_n is not a Galois subcover of the Hermitian curve. Finally, up to our knowledge, we find new values of the genus spectrum of F_q2n -maximal curves, by considering some Galois subcovers of X_n.