For every q=n^3 with n a prime power greater than 2, the GK-curve is an F_{q^2}-maximal curve that is not F_{q^2}-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are investigated. Infinitely many examples of maximal curves that cannot be Galois covered by the Hermitian curve are obtained. We also describe explicit equations for some families of quotient curves of the GK-curve. In several cases, such curves provide new values in the spectrum of genera of F_{q^2}-maximal curves.
Maximal curves from subcovers of the GK-curve
GIULIETTI, Massimo;ZINI, GIOVANNI
2016
Abstract
For every q=n^3 with n a prime power greater than 2, the GK-curve is an F_{q^2}-maximal curve that is not F_{q^2}-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are investigated. Infinitely many examples of maximal curves that cannot be Galois covered by the Hermitian curve are obtained. We also describe explicit equations for some families of quotient curves of the GK-curve. In several cases, such curves provide new values in the spectrum of genera of F_{q^2}-maximal curves.File in questo prodotto:
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