𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Curves with Many Points and Configurations of Hyperplanes over Finite Fields

✍ Scribed by Ferruh Özbudak; Henning Stichtenoth

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
147 KB
Volume
5
Category
Article
ISSN
1071-5797

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

On Drinfeld Modular Curves with Many Rat
On Drinfeld Modular Curves with Many Rational Points over Finite Fields
✍ Andreas Schweizer 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 137 KB

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

Counting Points on Curves and Abelian Va
Counting Points on Curves and Abelian Varieties Over Finite Fields
✍ Leonard M. Adleman; Ming-Deh Huang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 343 KB

We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space over Fq, we improve Pila's result and show that the pro

Curves of Every Genus with Many Points,
Curves of Every Genus with Many Points, I: Abelian and Toric Families
✍ Andrew Kresch; Joseph L. Wetherell; Michael E. Zieve 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 157 KB

Let N q g denote the maximal number of F q -rational points on any curve of genus g over F q . Ihara (for square q) and Serre (for general q) proved that lim sup g→∞ N q g /g > 0 for any fixed q. Here we prove lim g→∞ N q g = ∞. More precisely, we use abelian covers of P 1 to prove lim inf g→∞ N q g

Curves with Many Points and Multiplicati
Curves with Many Points and Multiplication Complexity in Any Extension of Fq
✍ Stéphane Ballet 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 157 KB

From the existence of algebraic function "elds having some good properties, we obtain some new upper bounds on the bilinear complexity of multiplication in all extensions of the "nite "eld % O , where q is an arbitrary prime power. So we prove that the bilinear complexity of multiplication in the "n