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Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensions

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Book cover Algorithmic Number Theory (ANTS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1838))

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Abstract

A general type of ray class fields of global function fields is investigated. The computation of their genera is reduced to the determination of the degrees of these extensions, which turns out to be the main difficulty. While in two special situations explicit formulas for the degrees are known, the general problem is solved algorithmically. The systematic application of the methods described yields several new examples of algebraic curves over \(\mathbb{F}_{2}, \mathbb{F}_{3}, \mathbb{F}_{4}, \mathbb{F}_{5}\) and \( \mathbb{F}_{7}\) with comparatively many rational points.

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Author information

Authors and Affiliations

  1. Rijksuniversiteit Groningen, Vakgroep Wiskunde, Blauwborgje 3, NL-9747 AC, Groningen, The Netherlands

    Roland Auer

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  1. Roland Auer
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Editor information

Editors and Affiliations

  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Wieb Bosma

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Auer, R. (2000). Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensions. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_6

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  • DOI: https://doi.org/10.1007/10722028_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67695-9

  • Online ISBN: 978-3-540-44994-2

  • eBook Packages: Springer Book Archive

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