# 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:

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What do you want to do with them? Meanwhile, see ams.org/bookstore-getitem/item=GSM-67 – Will Jagy Dec 6 '12 at 5:59
thank you. it helps me very much. – Mj125 Dec 6 '12 at 6:51
For the curious, see well-informed answer at mathoverflow.net/questions/115573/… – Will Jagy Dec 6 '12 at 18:27