Adv. Math. Commun., 2012
Fanali, S., Giulietti, M., & Platoni, I. (2012). On maximal curves over finite fields of small order. Adv. Math. Commun.
Fanali, S., M. Giulietti, and Irene Platoni. “On Maximal Curves over Finite Fields of Small Order.” Adv. Math. Commun. (2012).
Fanali, S., et al. “On Maximal Curves over Finite Fields of Small Order.” Adv. Math. Commun., 2012.
We show that there exists a unique maximal curve of genus $7$ over the finite field with $49$ elements, up to birational equivalence. This was the first open classification problem for maximal curves, since maximal curves over the finite fields with less than $49$ elements, as well as maximal curves over the finite field with $49$ elements with genus larger than $7$, had been previously classified. A significant role is played by some exhaustive computer searches.