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We establish small correlation bounds for the Moebius function and the Walshsystem, answering affirmatively a question posed by G.Kalai [Ka]. The argumentis based on generalizing the approach of Mauduit and Rivat [M-R] in order totreat Walsh functions of `large weight', while the `small weight' case followsfrom recent work due to B.Green [Gr]. The conclusion is an estimate uniformover the full Walsh system. A similar result also holds for the Liouvillefunction.

Moebius-Walsh correlation bounds and an estimate of Mauduit and Rivat