ELEMENTARY ABELIAN P-EXTENSIONS AND CURVES WITH MANY POINTS
Vol. 36 No. 139 (2012), Mathematics
Vol. 36 No. 139 (2012)

ELEMENTARY ABELIAN P-EXTENSIONS AND CURVES WITH MANY POINTS

Mathematics
https://doi.org/10.18257/raccefyn.36(139).2012.2453
Published 2023-12-22
Alvaro Garzón R.
Departamento de Matem´aticas, Universidad del Valle, Apartado A´ereo 25360, Cali, Colombia
Arnoldo Teherán Herrera
Universidad Industrial de Santander. Bucaramanga, Colombia.
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How to Cite

Garzón R., A., & Teherán Herrera, A. (2023). ELEMENTARY ABELIAN P-EXTENSIONS AND CURVES WITH MANY POINTS. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 36(139), 243–252. https://doi.org/10.18257/raccefyn.36(139).2012.2453
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Abstract

In the paper we give a generalization of two results of two results obtained by García and Stichtenoth  ([G-S]) and use them of exhibit a method to construct curves over finite fields whose number of rational points is large compared to their genus. Such curves are induced by algebraic functions fields obtained from elementary abelain p-extensions of the rational function field Fq(x) using the trace operator TrFq/Fp.

https://doi.org/10.18257/raccefyn.36(139).2012.2453

Keywords

Finite fields | Algebraic curves | Algebraic Function Fields | Elementary | Abelain p Extensions | Rational Points
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References

[G-S] Garcia and Stichtenoth. Elementary abelian p- extension of algebraic functions fileds. Manuscripta mathematica, Springer-Verlag. pag 67-79, 1991.

[L-N] Lidl Rudolf and Niederreiter Harald. Introduction to finite and their applications. Cambridge university press, 1994.

[Go] V.D. Goppa. Copes on algebraic curves. Sov Math. Doki 24 (1981), 170-172.

[La] Lang Serge, Algebra, Adisson Wesley Publishing Company, 1970.

[Ka] Kani Ernesy, Relations between the genera and between the Hasse-Witt invariants of Galois covering of curves, Canad. Math. Bull, Vol 28, pag 31-327, 1985.

[N-CH] Harald Niederreiter, Huaxiong Wanf and Chaoping Xing, Function Fields over Finite Fields and their applicatios to Cryptography. Topics in Geometry, Coding Theory and Cryptography, Springer-Verlag. 2007.

[I] Ihara Y. Some remarks on number of rational points of algebraic curves over finite fields. J Fac Sci Tokyio 28(1981), p 721-724.

[Ro] Roman Steve. Field Theory. Springer-Verlag, 1991 .

[ST] Stichtenoth Henning. Algebraic funtions field and codes. Springer-Verlag, 1993.

[VV] Van Der Geer Gerard and Van Der Vlugt Marcel. Tables of curves with many points [Online], http://www.science.uva.nl/geer.

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