Uma caracterização da planaridade de uma família de funções binomiais sobre corpos finitos via curvas algébricas
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| Main Author: | |
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| Publication Date: | 2022 |
| Format: | Master thesis |
| Language: | por |
| Source: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/12326 |
Summary: | In this work, we study a family of binomial functions given by $$ f_{a,b}(x)=ax^{2^{2^m}+1}+bx^{2^m+1}, \quad \mbox{with } \ a,b\in\mathbb{F}_{q^3}^\times, $$ 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 $(a,b)\in(\mathbb{F}_{q^3}^\times)^2$ such that the function $f_{a,b}(x)$ is planar. |