How to find orthogonal subspace of a subspace

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You can use the method complement. In your case:

sage: U_perp = U.complement()
sage: U_perp
Vector space of degree 4 and dimension 2 over Finite Field of size 2
Basis matrix:
[1 1 0 0]
[0 0 0 1]

We can easily check that this is indeed the orthogonal complement:

sage: [ b*c for b in U_perp.basis() for c in U.basis() ]
[0, 0, 0, 0]