𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Fibre products of Kummer covers and curves with many points

✍ Scribed by Ferruh Özbudak; Burcu Gülmez Temur

Publisher
Springer
Year
2007
Tongue
English
Weight
158 KB
Volume
18
Category
Article
ISSN
0938-1279

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Curves with Many Points and Configuratio
Curves with Many Points and Configurations of Hyperplanes over Finite Fields
✍ Ferruh Özbudak; Henning Stichtenoth 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 147 KB

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.

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