# two non-degenerate quadratic forms on $GF(2)^2r$

I know this:

There are two non-degenerate quadratic forms on $GF(2)^2r$. The hyperbolic form may be taken to be $Q^+(x)=x_0 x_1 + \cdots +x_{2r-2}x_{2r-1}$ ,

and the elliptic form to be

$Q^-(x)=x^2_0 +x_0x_1 +x^2_1 +x_2x_3 + \cdots +x_{2r-2}x_{2r-1}$.

and my question is: