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Lecture 4 Almost k-wise Independent Variables

We will now consider the problem of creating a set of bitstrings such that the bits are almost k-wise independent. Our method consists of two steps. In the first step we create a set of bitstrings such that parity on every fixed index set is almost even. In the second step we present a method to convert such a set into a set where the bits are almost k-wise independent. For presentational reasons we give the steps in reverse order, i.e., we start by showing how to create almost k-wise indpendent bitstrings from a set with almost even parity.