On Rigid Matrices and U-Polynomials
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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.
KeywordsMatrix rigidity small-bias sets unbalanced expanders
Subject classification68Q17 68R05
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