vix.ing · top · new · best · stats · spec

Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

2011/01/24 by Francis N. Castro, Castro, Francis N., Luis A. Medina +1
Computer Science · Mathematics · #05E05 #11T23 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:05E05 #msc:11T23

paper · pdf · doi:10.48550/arxiv.1101.4682

18 pages, 3 figures

arxiv created 2011/01/24 · openalex publication_date 2011/01/24 · arxiv updated 2011/01/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than 2n.

Related