## Conference "Arithmetic, Geometry and Coding Theory"## March 14 - 18, 2011## CIRM, Marseille, France |

**Organisers:** Yves Aubry *(Université de la Méditerranée, IML)*, Christophe Ritzenthaler *(Université de la Méditerranée, IML)*, Alexey Zykin *(Mathematical Department of HSE, Laboratoire Poncelet, IITP)*

We show that the generalized Giulietti-Korchmaros curve (GK curve) and the maximal curve with equation x^{q^2}-x = y^{(q^n+1)/(q+1)} defined over the finite field of q^{2n} elements, for n \geq 3 odd and q \geq 3, are not Galois subcovers of the Hermitian curve over the same finite field. For q = 2, we show that the generalized GK curve is covered by the Hermitian curve. This is joint work with Iwan Duursma.