Curves with Many Points and Configurations of Hyperplanes over Finite Fields

We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterlé b...

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Bibliographic Details
Published in:Finite fields and their applications 1999-10, Vol.5 (4), p.436-449
Main Authors: Özbudak, Ferruh, Stichtenoth, Henning
Format: Article
Language:English
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Summary:We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterlé bound.
ISSN:1071-5797
1090-2465
DOI:10.1006/ffta.1999.0262