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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
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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 …