scholarly journals Modular periodicity of exponential sums of symmetric Boolean functions

2017 ◽  
Vol 217 ◽  
pp. 455-473 ◽  
Author(s):  
Francis N. Castro ◽  
Luis A. Medina
Keyword(s):  
Boolean Functions ◽  
Exponential Sums ◽  
Symmetric Boolean Functions ◽  
Modular Periodicity

scholarly journals Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions

10.37236/2004 ◽  
2011 ◽  
Vol 18 (2) ◽  
Author(s):  
Francis N. Castro ◽  
Luis A. Medina
Keyword(s):  
Asymptotic Behavior ◽  
Boolean Functions ◽  
Exponential Sums ◽  
Exponential Sum ◽  
Linear Recurrence ◽  
Symmetric Boolean Function ◽  
Linear Recurrences ◽  
Symmetric Boolean Functions ◽  
Integer Coefficients ◽  
Homogeneous Linear

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 $2^n$.

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