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arXiv · 1709.00752

A short note on the joint entropy of n/2-wise independence

Amey Bhangale·Aditya Potukuchi
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Abstract

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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Amey Bhangale, Aditya Potukuchi. 2018-01-12. A short note on the joint entropy of n/2-wise independence. https://arxiv.org/abs/1709.00752

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