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The genus of curves over finite fields with many rational points

✍ Scribed by Rainer Fuhrmann; Fernando Torres

Book ID
110558267
Publisher
Springer
Year
1996
Tongue
English
Weight
157 KB
Volume
89
Category
Article
ISSN
0025-2611

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πŸ“œ SIMILAR VOLUMES

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It is known that Drinfeld modular curves can be used to construct asymptotically optimal towers of curves over finite fields. Using reductions of the Drinfeld modular curves X 0 ðnÞ, we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin

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We give a simple and e ective method for the construction of algebraic curves over ΓΏnite ΓΏelds with many rational points. The curves constructed are Kummer covers or ΓΏbre products of Kummer covers of the projective line.

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We establish a correspondence between a class of Kummer extensions of the rational function "eld and con"gurations of hyperplanes in an a$ne space. Using this correspondence, we obtain explicit curves over "nite "elds with many rational points. Some of our examples almost attain the OesterleH bound.