Finite number of fibre products of Kummer covers and curves with many points over finite fields

ÖZBUDAK F., GÜLMEZ TEMÜR B.

DESIGNS CODES AND CRYPTOGRAPHY, vol.70, no.3, pp.385-404, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 3
  • Publication Date: 2014
  • Doi Number: 10.1007/s10623-012-9706-2
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.385-404
  • Middle East Technical University Affiliated: Yes

Abstract

We study fibre products of a finite number of Kummer covers of the projective line over finite fields. We determine the number of rational points of the fibre product over a rational point of the projective line, which improves the results of Ozbudak and Temur (Appl Algebra Eng Commun Comput 18:433-443, 2007) substantially. We also construct explicit examples of fibre products of Kummer covers with many rational points, including a record and two new entries for the current table (http://www.manypoints.org, 2011).