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Bounds on the Fourier Coefficients of the Weighted Sum Function
"... We estimate Fourier coefficients of a Boolean function which has recently been introduced in the study of readonce branching programs. Our bound implies that this function has an asymptotically “flat ” Fourier spectrum and thus implies several lower bounds of its various complexity measures. ..."
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We estimate Fourier coefficients of a Boolean function which has recently been introduced in the study of readonce branching programs. Our bound implies that this function has an asymptotically “flat ” Fourier spectrum and thus implies several lower bounds of its various complexity measures.
Laced Boolean functions and subset sum problems in finite fields
, 2011
"... In this paper, we investigate some algebraic and combinatorial properties of a special Boolean function on n variables, defined using weighted sums in the residue ring modulo the least prime p ≥ n. We also give further evidence to a question raised by Shparlinski regarding this function, by comput ..."
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In this paper, we investigate some algebraic and combinatorial properties of a special Boolean function on n variables, defined using weighted sums in the residue ring modulo the least prime p ≥ n. We also give further evidence to a question raised by Shparlinski regarding this function, by computing accurately the Boolean sensitivity, thus settling the question for prime number values p = n. Finally, we propose a generalization of these functions, which we call laced functions, and compute the weight of one such, for every value of n.