Boolean Functions and Permanents of Sylvester Hadamard Matrices

José Andrés Armario
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José Andrés Armario: Departamento de Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012 Sevilla, Spain

Mathematics, 2021, vol. 9, issue 2, 1-8

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 2 m , H m , can be carried out by enumerating m -variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient p e r ( H m ) / 2 2 m might be a measure of the “density” of m -variable Boolean functions with high nonlinearity.

Keywords: permanent; Sylvester Hadamard matrices; Ryser’s formula; Boolean functions; Walsh spectrum; high nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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