On maximal curves that are not quotients of the Hermitian curve

Massimo Giulietti, Maria Montanucci, Giovanni Zini

For each prime power $\ell$ the plane curve ${\mathcal{X}}_{\ell }$ with equation $Y^{{\ell }^2-\ell +1}=X^{{\ell }^2}-X$ is maximal over ${\mathbb{F}}_{{\ell }^6}$. Garcia and Stichtenoth in 2006 p…