Curves with many points and configurations of hyperplanes over finite fields

Ozbudak F. , Stichtenoth H.

FINITE FIELDS AND THEIR APPLICATIONS, vol.5, no.4, pp.436-449, 1999 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 1999
  • Doi Number: 10.1006/ffta.1999.0262
  • Title of Journal : FINITE FIELDS AND THEIR APPLICATIONS
  • Page Numbers: pp.436-449

Abstract

We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.