Exponential Correlation Bounds for Polynomials
arXiv:2609.28839
Abstract
We prove that the XOR of majorities on disjoint blocks of \(\ell\) bits has correlation at most \((2d/\sqrt{\ell})^k\) with every degree-\(d\) polynomial over \(\mathbb F_2\). By known techniques, this implies pseudorandom generators with polylogarithmic seed length for low-degree polynomials over and for alternating circuits with parity gates.
12 pages