Abstract
We show that, under certain conditions, restricted and biased exponential sums and Walsh transforms of symmetric and rotation symmetric Boolean functions are, as in the case of nonbiased domain, -finite sequences. We also prove that under other conditions, these sequences are -finite, which is a somewhat different behavior than their nonbiased counterparts. We further show that exponential sums and Walsh transforms of a family of rotation symmetric monomials over the restricted domain ( is the weight of the vector ) are given by polynomials of degree at most , and so, they are also -finite sequences. Finally, we also present a study of the behavior of symmetric Boolean functions under these biased transforms.
Citation
Axel O. Gómez-Flores. Luis A. Medina. Pantelimon Stănică. "Recursions for modified Walsh transforms of some families of Boolean functions." Rocky Mountain J. Math. 52 (4) 1355 - 1373, August 2022. https://doi.org/10.1216/rmj.2022.52.1355
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