Complete arcs arising from a generalization of the Hermitian curve
Herivelto Borges, Beatriz Motta, Fernando Torres · Scientific Electronic Library Online (São Paulo Research Foundation, Latin American and Caribbean Center on Health Sciences Information, Conselho Nacional de Desenvolvimento Científico e Tecnológico) · 2014
We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin–Schreier curves, which is calculated by using exponential sums via Coulter's approach. We also single out some examples of maximal curves.