A family of Kummer covers over the hermitian function field

Published

2008-01-01

A family of Kummer covers over the hermitian function field

Una familia de cubrimientos de Kummer sobre el campo de funciones hermitianas

Keywords:

Finite fields, algebraic function fields, rational places, hermitian function field, Kummer extensions, 2000 Mathematics Subject Classification. 14G05 (en)
Campos finitos, campos de funciones algebraicas, lugares racionales, campos de funciones hermitianas, extensiones de Kummer (es)

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Universidad del Valle, Cali, Colombia

Abstract (en)
Abstract (es)

Abstract. We construct a family of Kummer covers o v e r the Hermitian Function Field by using a class of polynomials Ƭ₂(X, Y) wich arises as a generalization of certain simmetryc polynomials S₂(X). The number of rational places of such covers is often rather close to the best value listed in [6].

Construimos una familia de cubrimientos Kummer sobre el cuerpo de las funciones Hermitianas usando una clase de polinomios Ƭ₂(X, Y) que surge como una generalización de cierto tipo de polinomios S₂(X). El número de lugares racionales de tales cubrimientos es cercano al mejor valor que se encuentra en [6].

References

Garcia, A., and Stichtenoth, H. A class of polynomials over finite fields. Finite Fields and Their Appl. 5 (1999), 424-435.

Garzón, A. Homogenized polynomials and curves with many points. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales XXX, 117 (2006), 555-561.

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

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

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

Van der Geer, G., and Van der Vlugt, M . Tables for the function Nq(g).

How to Cite

APA

Álvaro. (2008). A family of Kummer covers over the hermitian function field. Revista Colombiana de Matemáticas, 42(1), 73–84. https://revistas.unal.edu.co/index.php/recolma/article/view/94995

ACM

[1]

Álvaro 2008. A family of Kummer covers over the hermitian function field. Revista Colombiana de Matemáticas. 42, 1 (Jan. 2008), 73–84.

ACS

(1)

Álvaro. A family of Kummer covers over the hermitian function field. rev.colomb.mat 2008, 42, 73-84.

ABNT

ÁLVARO. A family of Kummer covers over the hermitian function field. Revista Colombiana de Matemáticas, [S. l.], v. 42, n. 1, p. 73–84, 2008. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94995. Acesso em: 22 jan. 2025.

Chicago

Álvaro. 2008. “A family of Kummer covers over the hermitian function field”. Revista Colombiana De Matemáticas 42 (1):73-84. https://revistas.unal.edu.co/index.php/recolma/article/view/94995.

Harvard

Álvaro (2008) “A family of Kummer covers over the hermitian function field”, Revista Colombiana de Matemáticas, 42(1), pp. 73–84. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94995 (Accessed: 22 January 2025).

IEEE

[1]

Álvaro, “A family of Kummer covers over the hermitian function field”, rev.colomb.mat, vol. 42, no. 1, pp. 73–84, Jan. 2008.

MLA

Álvaro. “A family of Kummer covers over the hermitian function field”. Revista Colombiana de Matemáticas, vol. 42, no. 1, Jan. 2008, pp. 73-84, https://revistas.unal.edu.co/index.php/recolma/article/view/94995.

Turabian

Álvaro. “A family of Kummer covers over the hermitian function field”. Revista Colombiana de Matemáticas 42, no. 1 (January 1, 2008): 73–84. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94995.

Vancouver

1.

Álvaro. A family of Kummer covers over the hermitian function field. rev.colomb.mat [Internet]. 2008 Jan. 1 [cited 2025 Jan. 22];42(1):73-84. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/94995