Frobenius nonclassicality of Fermat curves with respect to cubics

Nazar Arakelian, Herivelto Borges

For Fermat curves $\mathcal{F}:a{X}^n+b{Y}^n=Z^n$ defined over ${\mathbb{F}}_q$, we establish necessary and sufficient conditions for $\mathcal{F}$ to be ${\mathbb{F}}_q$-Frobenius nonclas…