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

Let F-q be a finite field of characteristic 2, not containing F-4. Let k >= 2 be an even 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. We apply this to the classification of maximal and minimal curves over finite fields