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{\bf Francis N. Castro and Luis A. Medina}
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{\bf Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions}
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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 $2^n$.

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