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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 4
  • Publication Date: 1999
  • Doi Number: 10.1006/ffta.1999.0262
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.436-449
  • Middle East Technical University Affiliated: Yes

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.