Geodesic
Complete arcs arising from a generalization of the Hermitian curve
Herivelto Borges 1   ; Beatriz Motta 2   ; Fernando Torres 3
1 Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo 13560-970, São Carlos, SP, Brazil
2 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
3 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
Acta Arithmetica, Tome 164 (2014) no. 2, pp. 101-118 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa164-2-1
Keywords: investigate complete arcs degree greater projective planes finite fields arising set rational points generalization hermitian curve degree arcs closely related number rational points class artin schreier curves which calculated using exponential sums via coulters approach single out examples maximal curves

Herivelto Borges  1   ; Beatriz Motta  2   ; Fernando Torres  3

1 Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo 13560-970, São Carlos, SP, Brazil
2 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
3 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 
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     author = {Herivelto Borges and Beatriz Motta and Fernando Torres},
     title = {Complete arcs arising from a generalization of the {Hermitian} curve},
     journal = {Acta Arithmetica},
     pages = {101--118},
     year = {2014},
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     doi = {10.4064/aa164-2-1},
     language = {en},
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Herivelto Borges; Beatriz Motta; Fernando Torres. Complete arcs arising from a generalization of the Hermitian curve. Acta Arithmetica, Tome 164 (2014) no. 2, pp. 101-118. doi: 10.4064/aa164-2-1

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