Complete arcs arising from a generalization of the Hermitian curve

Autor(es)

Borges, Herivelto ^[1] ; Motta, Beatriz ^[2] ; Torres, Fernando ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Fed Juiz de Fora, Inst Ciencias Exatas, Dept Matemat, BR-36036900 Juiz De Fora, MG - Brazil

^[3] Univ Estadual Campinas, UNICAMP, Inst Math Stat & Comp Sci IMECC, BR-13083059 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ACTA ARITHMETICA; v. 164, n. 2, p. 101-118, 2014.
• Citações Web of Science: 1

Resumo

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. (AU)

• Processo FAPESP: 11/19446-3 - Curvas algébricas sobre corpos finitos
• Beneficiário: Herivelto Martins Borges Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular