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On Rigid Matrices and UPolynomials
, 2012
"... We introduce a class of polynomials, which we call Upolynomials 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 smallbias sets are hitting sets for the class of Upolynomi ..."
Abstract

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We introduce a class of polynomials, which we call Upolynomials 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 smallbias sets are hitting sets for the class of Upolynomials, though their size is larger than desired. Furthermore, we give two alternative proofs for the fact that smallbias sets induce rigid matrices. Finally, we construct rigid matrices from unbalanced expanders, with essentially the same size as the construction via smallbias sets.