  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.
