For every q = 3 with a prime power greater than 2, the GK curve X is an F_q^2-maximal curve that is not F_q^2 -covered by any F_q^2-maximal Deligne–Lusztig curve. Interestingly, X has a very large F_q^2-automorphism group with respect to its genus. In this paper we compute the genera of a large variety of curves that are Galois-covered by the GK curve, thus providing several new values in the spectrum of genera of F_q^2-maximal curves.
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