Complete arcs arising from a generalization of the Hermitian curve

Herivelto Borges; Beatriz Motta; Fernando Torres

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arXiv · 1401.3702

Complete arcs arising from a generalization of the Hermitian curve

Herivelto Borges·Beatriz Motta·Fernando Torres

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Abstract

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.

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Herivelto Borges, Beatriz Motta, Fernando Torres. 2014-01-15. Complete arcs arising from a generalization of the Hermitian curve. https://arxiv.org/abs/1401.3702

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