Subsets of F2 that are ε-biased, meaning that the parity of any set of bits is even or odd with probability ε close to 1/2, are powerful tools for derandomization. A simple randomized construction shows that such sets exist of size O(n/ε), and known deterministic constructions achieve sets of size O(n/ε), O(n/ε), and O((n/ε)). Rather than derandomizing… (More)

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