%0 Journal Article %1 bhangale2017short %A Bhangale, Amey %A Potukuchi, Aditya %D 2017 %K entropy-inequalities %T A short note on the joint entropy of n/2-wise independence %U http://arxiv.org/abs/1709.00752 %X 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.

@article{bhangale2017short, 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 Pudl\'ak.}, added-at = {2018-01-17T23:00:28.000+0100}, author = {Bhangale, Amey and Potukuchi, Aditya}, biburl = {https://www.bibsonomy.org/bibtex/245ed45127a145a153ab6eb03d1e54a7b/claired}, description = {A short note on the joint entropy of n/2-wise independence}, interhash = {2966127eeea4778b008910d91c40fbe6}, intrahash = {45ed45127a145a153ab6eb03d1e54a7b}, keywords = {entropy-inequalities}, note = {cite arxiv:1709.00752Comment: 6 pages, some errors fixed}, timestamp = {2018-01-17T23:00:28.000+0100}, title = {A short note on the joint entropy of n/2-wise independence}, url = {http://arxiv.org/abs/1709.00752}, year = 2017 }