Subspace Evasive Sets

We construct explicit subspace-evasive sets. These are subsets of Fn of size |F|(1-ε)n whose intersection with any k-dimensional subspace is bounded by a constant c(k,ε). This problem was raised by Guruswami (CCC 2011) as it leads to optimal rate list-decodable codes of constant list size. The main technical ingredient is the construction of k low-degree polynomials whose common set of zeros has small intersection with any k-dimensional subspace.

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