Curves related to Coulter's maximal curves

ÇAKÇAK E., ÖZBUDAK F.

FINITE FIELDS AND THEIR APPLICATIONS, vol.14, no.1, pp.209-220, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.1016/j.ffa.2006.10.003
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.209-220
  • Middle East Technical University Affiliated: Yes

Abstract

We study a class of curves over finite fields such that the maximal (respectively minimal) curves of this class form a subclass containing the set of maximal (respectively minimal) curves of Coulter (cf. [R.S. Coulter, The number of rational points of a class of Artin-Schreier curves, Finite Fields Appl. 8 (2002) 397-413, Theorem 8.12]) as a proper subset. We determine the exact number of rational points of the curves in the class and we characterize maximal (respectively minimal) curves of the class as subcovers of some suitable curves. In particular we show that Coulter's maximal curves are Galois subcovers of the appropriate Hermitian curves. (c) 2006 Elsevier Inc. All rights reserved.