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.
Texto completo disponible en PDF
References
[1] A. García and H. Stichtenoth, `A Class of Polynomials over Finite Fields', Finite Fields and Their Applications 5, (1999), 424-435.
[2] A. Garzón, `Euclidean Algorithm and Kummer Covers with many Points', Revista Colombiana de Matemáticas 37, 1 (2003), 37-50.
[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.
[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.
[5] H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, Germany, 1993.
[6] G. Van der Geer and M. Van der Vlugt, `Kummers Covers with many Points', Finite Fields and their Appl., (2000), 327-341.
[7] G. Van der Geer and M. Van der Vlugt, Tables with many Points, (2013). available in http://manypoints.org.
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCMv47n2a02,
AUTHOR = {Garzón, Álvaro and Navarro, Horacio},
TITLE = {{Division Algorithm and Construction of Curves with Many Points}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2013},
volume = {47},
number = {2},
pages = {131--147}
}