How can you find all of the solutions of a quadratic equation $x^t A x = g$ over a field with a characteristic 2 in a polynomial numbers of operations (specifically $GF(2)$)?
In a field with a characteristic $\not= 2$ this can be solved by representing the quadratic form in a diagonal matrix over some base, and solving $x_1^2 + x_2^2 + ... = g$, but in a field with characteristic a quadratic form doesn't always have a diagonal matrix. How can you solve it in that case in a polynomial numbers of operations?