Before revision:  Moreover, we also show that the same is true for computing the Tutte polynomial of a binary matroid of dimension k on k^{O(1)} points with at most three nonzero coordinates in each point's vector.
After revision:  We also show that the same is true for computing the Tutte polynomial of a binary matroid of dimension k on k^{O(1)} points with at most three nonzero coordinates in each point's vector.