Quadratic forms of codimension 2 over certain finite fields of even characteristic

Authors:
Ferruh Özbudak;Elif Saygı;Zülfükar Saygı
Affiliations:
Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey 06800;Primary Mathematics Education Division, Department of Primary Education, Faculty of Education, Hacettepe University, Ankara, Turkey 06550;Department of Mathematics, TOBB University of Economics and Technology, Ankara, Turkey 06530
Venue:
Cryptography and Communications
Year:
2011

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Abstract

Let ${\mathbb F}_q$ be a finite field of characteristic 2, not containing ${\mathbb F}_4$ . Let k驴驴驴2 be an even integer. We give a full classification of quadratic forms over ${\mathbb F}_{q^k}$ of codimension 2 provided that certain three coefficients are from ${\mathbb F}_4$ . We apply this to the classification of maximal and minimal curves over finite fields.