  We describe a new statistical test for pseudorandom number generators
(PRNGs). Our test can find bias induced by dependencies among the Hamming
weights of the outputs of a PRNG, even for PRNGs that pass state-of-the-art
tests of the same kind from the literature, and in particular for generators
based on $\mathbf F_2$-linear transformations such as the dSFMT,
xoroshiro1024+, and WELL512.
