A short note on the joint entropy of n/2-wise independence
Amey Bhangale, Aditya Potukuchi · arXiv (Cornell University) · 2017
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.