Vol. 1, No. 1, 2013

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Computing equations of curves with many points

Virgile Ducet and Claus Fieker

Vol. 1 (2013), No. 1, 317–334
Abstract

We explain how to compute the equations of the abelian coverings of any curve defined over a finite field. Then we describe an algorithm which computes curves with many rational points with respect to their genus. The implementation of the algorithm provides seven new records over F2.

Keywords
explicit class field theory, Kummer theory, Witt vectors, curves with many points, equations of abelian coverings
Mathematical Subject Classification 2010
Primary: 11R37
Secondary: 14H45
Milestones
Published: 14 November 2013
Authors
Virgile Ducet
Institut de Mathématiques de Luminy
Campus de Luminy, Case 907
13288 Marseille Cedex 9
France
Claus Fieker
Fachbereich Mathematik
Universität Kaiserslautern
Postfach 3049
67653 Kaiserslautern
Germany