¹Universidad del Valle, Cali, Colombia. Email: alvaro.garzon@correounivalle.edu.co
²Universidad del Valle, Cali, Colombia. Email: horacio.navarro@correounivalle.edu.co

We give a simple and effective method for the construction of algebraic curves over finite fields with many rational points. The curves are given as Kummer covers of the projective line.

Key words: Algebraic curves, Finite fields, Rational points, Kummer extensions.

Se presenta un simple y efectivo método para la construcción de curvas algebraicas sobre campos finitos con muchos puntos racionales. Las curvas son dadas como coberturas de Kummer de la línea proyectiva.

Palabras clave: Curvas algebraicas, campos finitos, puntos racionales, extensiones de Kummer.

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References

[1] A. García and H. Stichtenoth, `A Class of Polynomials over Finite Fields´, Finite Fields and Their Applications 5, (1999), 424-435.         [ Links ]

[2] A. Garzón, `Euclidean Algorithm and Kummer Covers with many Points´, Revista Colombiana de Matemáticas 37, 1 (2003), 37-50.         [ Links ]

[3] A. Garzón and A. García, `On Kummer Covers with many Points over Finite Fields´, Journal of Pure and Applied Algebra 185, (2003), 177-192.         [ Links ]

[4] H. Niederreiter and C. Xing, Rational Points on Curves over Finite Fields. Theory and Applications, `LMS Lecture Note Series 285´, 2001, Cambridge University Press.         [ Links ]

[5] H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, Germany, 1993.         [ Links ]

[6] G. Van der Geer and M. Van der Vlugt, `Kummers Covers with many Points´, Finite Fields and their Appl., (2000), 327-341.         [ Links ]

[7] G. Van der Geer and M. Van der Vlugt, Tables with many Points, (2013). available in http://manypoints.org.         [ Links ]

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