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

Özbudak, Ferruh
Saygi, Zulfukar
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).