ON THE NUMBER OF QUADRATIC FORMS HAVING CODIMENSION 2 RADICALS IN CHARACTERISTIC 2 GIVING MAXIMAL/MINIMAL CURVES


ÖZBUDAK F., SAYGI Z.

COMMUNICATIONS IN ALGEBRA, vol.42, no.9, pp.3795-3810, 2014 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 9
  • Publication Date: 2014
  • Doi Number: 10.1080/00927872.2013.795577
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.3795-3810

Abstract

Let F-q be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on F-q(k) over F-q such that the corresponding curve is maximal or minimal. This problem is first attempted in [3], in which the number of maximal curves is obtained only for (q, k) = (2, 6) and (q, k) = (2, 8).