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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-1,
author = {Herivelto Borges and Beatriz Motta and Fernando Torres},
title = {Complete arcs arising from a generalization of the Hermitian curve},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {101-118},
zbl = {1316.05020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-1}
}
Herivelto Borges; Beatriz Motta; Fernando Torres. Complete arcs arising from a generalization of the Hermitian curve. Acta Arithmetica, Tome 166 (2014) pp. 101-118. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-1/