Euclidean algorithm and Kummer covers with many points

Published

2003-01-01

Euclidean algorithm and Kummer covers with many points

Keywords:

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

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Authors

Universidad del Valle

Abstract (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.

References

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

How to Cite

APA

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]

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

ACS

(1)

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

ABNT

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 jan. 2025.

Chicago

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

Álvaro (2003) “Euclidean algorithm and Kummer covers with many points”, Revista Colombiana de Matemáticas, 37(1), pp. 37–50. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94280 (Accessed: 22 January 2025).

IEEE

[1]

Álvaro, “Euclidean algorithm and Kummer covers with many points”, rev.colomb.mat, vol. 37, no. 1, pp. 37–50, Jan. 2003.

MLA

Álvaro. “Euclidean algorithm and Kummer covers with many points”. Revista Colombiana de Matemáticas, vol. 37, no. 1, Jan. 2003, pp. 37-50, https://revistas.unal.edu.co/index.php/recolma/article/view/94280.

Turabian

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

Vancouver

1.

Álvaro. Euclidean algorithm and Kummer covers with many points. rev.colomb.mat [Internet]. 2003 Jan. 1 [cited 2025 Jan. 22];37(1):37-50. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/94280