Complete arcs arising from a generalization of the Hermitian curve
Volume 164 / 2014
Acta Arithmetica 164 (2014), 101-118
MSC: Primary 05B25, 11T23, 11T24; Secondary 14H25.
DOI: 10.4064/aa164-2-1
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.
