On Rigid Matrices and U-Polynomials - Alon, Noga; Cohen, Gil (Computational complexity, 2015)
We introduce a class of polynomials, which we call U - polynomials , and show that the problem of explicitly constructing a rigid matrix can be reduced to the problem of explicitly constructing a small hitting set for this class. We prove that small-bias sets are hitting sets for the class of U -polynomials, though their size is larger than desired. Furthermore, we give two alternative proofs for the fact that small-bias sets induce rigid matrices. Finally, we construct rigid matrices from unbalanced expanders, with essentially the same size as the construction via small-bias sets.