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 รฐnร, we try to find individual curves over finite fields with many rational points. The main idea is to divide by an Atkin
โฆ LIBER โฆ
A Formula for Constructing Curves over Finite Fields with Many Rational Points
โ Scribed by Kristin Lauter
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 143 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0022-314X
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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.