Uma caracterização da planaridade de uma família de funções binomiais sobre corpos finitos via curvas algébricas - Chu, Daniel (2022)
In this work, we study a family of binomial functions given by $$ f_{a,b}(x)=ax^{2^{2^m}+1}+bx^{2^m+1}, \quad with \ a,b\in\mathbb{F}_{q^3}^×, $$ over a finite field of characteristic 2. The aim consists to show that is possible to relate the planarity of the family above to a cubic plane projective curve $\mathcal{C}_{a,b}$. From this method, it is possible establish a characterization of the pairs $(a,b)\in(\mathbb{F}_{q^3}^×)^2$ such that the function $f_{a,b}(x)$ is planar.