A short note on the joint entropy of n/2-wise independence
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In this note, we prove a tight lower bound on the joint entropy of n unbiased Bernoulli random variables which are n/2-wise independent. For general k-wise independence, we give new lower bounds by adapting Navon and Samorodnitsky's Fourier proof of the `LP bound' on error correcting codes. This counts as partial progress on a problem asked by Gavinsky and Pudlák.
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