Boolean Functions and Permanents of Sylvester Hadamard Matrices
Mathematics2021Vol. 9(2), pp. 177–177
Citations Over TimeTop 20% of 2021 papers
Abstract
One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that this formula over Sylvester Hadamard matrices of order 2m, Hm, can be carried out by enumerating m-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient per(Hm)/22m might be a measure of the “density” of m-variable Boolean functions with high nonlinearity.
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