Maximal curves from subcovers of the GK-curve

Abstract

For every $q=n^3$ with $n$ a prime power greater than $2$, the GK-curve is an ${\mathbb{F}}_{q^2}$-maximal curve that is not ${\mathbb{F}}_{q^2}$-covered by the Hermitian curve. In this paper some Galois subcovers of the GK curve are investigated. We describe explicit equations for some families of quotients of the GK-curve. New values in the spectrum of genera of ${\mathbb{F}}_{q^2}$-maximal curves are obtained. Finally, infinitely many further examples of maximal curves that cannot be Galois covered by the Hermitian curve are provided.