Euclidean algorithm and Kummer covers with many points

Álvaro Garzón

Publicado

2003-01-01

Euclidean algorithm and Kummer covers with many points

Palabras clave:

Algebraic curves, Finite fields, Rational points, Kummer extensions, Mathematics Subject Classification. Primary: 14G05. (en)

Descargas

PDF (English)

Autores/as

Álvaro Garzón Universidad del Valle

Resumen (en)

Abstract.

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

Referencias

A. García & A Garzón, On Kummer Covers whith many Points, to appear in the Journal of Pure and Applied Algebra.

A. García & H. Stichtenoth, A Class of Polynomials over Finite Fields, Finite Fields and their Appl. 5 (1999), 4 24 -4 35.

A. García, H. Stichtenoth & C. P. Xing, On Subfields of the Hermitian Function Field, Compositio Math. 120 (2000), 137-170.

G Van der Geer & M. Van der Vlugt, Kummer Covers with many Rational Points, Finite Fields and their Appl. 6 (2000), 327-341.

G Van der Geer & M. Van der Vlugt, Tables for the function Nq(g), available at http://www.wins.uva.nl/~ geer.

H. Hasse, Theorie der relativ zyklischen algebraischen Funktionenkorper, J. Reine Angew. Math. 172 (1934), 37-54.

V. D. Goppa, Codes on algebraic curves. Sov. Math. Dokl. 24 (1981), 170-172.

Y. Ihara, Some remarks on the number of rational points of algebraic curves over finite Reids, J. Fac. Sei. Tokyo 28 (1981), 721-724.

R. Lil d & H. Niederreiter, Finite Fields and Applications, Cambridge Univ. Press, Cambridge, 1994.

H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 1993.

V. Shabat, Tables of curves with many points, available at the Web site http://www.wins.uva.nl/~shabat/tables.html

Cómo citar

APA

Garzón, Álvaro. (2003). Euclidean algorithm and Kummer covers with many points. Revista Colombiana de Matemáticas, 37(1), 37–50. https://revistas.unal.edu.co/index.php/recolma/article/view/94280

ACM

[1]

Garzón, Álvaro 2003. Euclidean algorithm and Kummer covers with many points. Revista Colombiana de Matemáticas. 37, 1 (ene. 2003), 37–50.

ACS

(1)

Garzón, Álvaro. Euclidean algorithm and Kummer covers with many points. rev.colomb.mat 2003, 37, 37-50.

ABNT

GARZÓN, Álvaro. Euclidean algorithm and Kummer covers with many points. Revista Colombiana de Matemáticas, [S. l.], v. 37, n. 1, p. 37–50, 2003. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94280. Acesso em: 22 ene. 2025.

Chicago

Garzón, Álvaro. 2003. «Euclidean algorithm and Kummer covers with many points». Revista Colombiana De Matemáticas 37 (1):37-50. https://revistas.unal.edu.co/index.php/recolma/article/view/94280.

Harvard

Garzón, Álvaro (2003) «Euclidean algorithm and Kummer covers with many points», Revista Colombiana de Matemáticas, 37(1), pp. 37–50. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94280 (Accedido: 22 enero 2025).

IEEE

[1]

Álvaro Garzón, «Euclidean algorithm and Kummer covers with many points», rev.colomb.mat, vol. 37, n.º 1, pp. 37–50, ene. 2003.

MLA

Garzón, Álvaro. «Euclidean algorithm and Kummer covers with many points». Revista Colombiana de Matemáticas, vol. 37, n.º 1, enero de 2003, pp. 37-50, https://revistas.unal.edu.co/index.php/recolma/article/view/94280.

Turabian

Garzón, Álvaro. «Euclidean algorithm and Kummer covers with many points». Revista Colombiana de Matemáticas 37, no. 1 (enero 1, 2003): 37–50. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94280.

Vancouver

1.

Garzón Álvaro. Euclidean algorithm and Kummer covers with many points. rev.colomb.mat [Internet]. 1 de enero de 2003 [citado 22 de enero de 2025];37(1):37-50. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/94280