Geodesic
Linear recurrences and asymptotic behavior of exponential sums of symmetric Boolean functions
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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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 $2^n$.
DOI : 10.37236/2004
Classification : 11T23, 05E05, 06E30
Mots-clés : exponential sums, recurrences, symmetric Boolean functions 
@article{10_37236_2004,
     author = {Francis N. Castro and Luis A. Medina},
     title = {Linear recurrences and asymptotic behavior of exponential sums of symmetric {Boolean} functions},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {2},
     doi = {10.37236/2004},
     zbl = {1250.11102},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/2004/}
}
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Francis N. Castro; Luis A. Medina. Linear recurrences and asymptotic behavior of exponential sums of symmetric Boolean functions. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2004

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