A New Test for Hamming-Weight Dependencies

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 particularly for generators based on F2-linear transformations such as the dSFMT [22], xoroshiro1024+ [1], and WELL512 [19].