Quadratic forms of codimension 2 over finite fields containing F-4 and Artin-Schreier type curves

ÖZBUDAK F., SAYGI E., Saygi Z.

FINITE FIELDS AND THEIR APPLICATIONS, vol.18, no.2, pp.396-433, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1016/j.ffa.2011.09.008
  • Journal Name: FINITE FIELDS AND THEIR APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.396-433
  • Middle East Technical University Affiliated: Yes

Abstract

Let F-q be a finite field containing F-4. Let k >= 2 be an integer. We give a full classification of quadratic forms over F-q(k) of codimension 2 provided that certain three coefficients are from F-4. As an application of this we obtain new results on the classification of maximal and minimal curves over F-q(k) . We also give some nonexistence results on certain systems of equations over F-q(k). (C) 2011 Elsevier Inc. All rights reserved.