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Complete arcs arising from a generalization of the Hermitian curve

Volume 164 / 2014

Herivelto Borges, Beatriz Motta, Fernando Torres 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.

Authors

  • Herivelto BorgesInstituto de Ciências Matemáticas
    e de Computação
    Universidade de São Paulo
    13560-970, São Carlos, SP, Brazil
    e-mail
  • Beatriz MottaDepartamento 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
    e-mail
  • Fernando TorresInstitute 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
    e-mail

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