Abstract:The absolute value distribution of the Walsh spectrums of Boolean functions is presented and studied. The absolute value distribution of the Walsh spectrum is invariant under affine transformations. Then Walsh spectrums' absolute value distributions of all n-variable Boolean functions are obtained for. The relationships of the absolute value distributions of the Walsh spectrums and the support of the Walsh spectrums and the number of nonzero values of the Walsh spectrums and other problems are studied. Finally, the size of the absolute value distribution of the Walsh spectrum of Boolean functions is studied.