Complete arcs arising from a generalization of the Hermitian curve

• Autorzy: Herivelto Borges , Beatriz Motta , Fernando Torres
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 14H25: Arithmetic ground fields
• 11T23: Exponential sums
• 11T24: Other character sums and Gauss sums
• 05B25: Finite geometries

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 2
• Strony: 101-118

Daty

wydano

2014

Twórcy

autor

Herivelto Borges

• Instituto de Ciências Matemáticas, e de Computação, Universidade de São Paulo, 13560-970, São Carlos, SP, Brazil

autor

Beatriz Motta

• Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Rua José Lourenço Kelmer s/n, Campus Universitário, Bairro São Pedro, 36036-900, Juiz de Fora, MG, Brazil

autor

Fernando Torres

• Institute of Mathematics, Statistics, and Computer Science (IMECC), University of Campinas (UNICAMP), R. Sérgio Buarque de Holanda, 651, Cidade Universitária "Zeferino Vaz", 13083-059, Campinas, SP, Brazil

Identyfikatory

DOI

10.4064/aa164-2-1