On maximal curves over finite fields of small order
Stefania Fanali, Massimo Giulietti, Irene Platoni · Advances in Mathematics of Communications · 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.