Geodesic
The sum of modules of Walsh coefficients of Boolean functions
Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 49-66

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We obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of $n$ variables. An average value of such sums in the class of all Boolean functions of $n$ variables and in its subclass consisting of all balanced functions is evaluated. We present some classes of nonlinear balanced functions whose sums of modules of Walsh coefficients are close to the obtained lower and upper bounds.
Keywords: Boolean functions, Walsh coefficients, filtering generators. 
@article{DM_2015_27_4_a4,
     author = {R. A. De La Krus Khimenes and O. V. Kamlovskii},
     title = {The sum of modules of {Walsh} coefficients of {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {49--66},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_4_a4/}
}
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R. A. De La Krus Khimenes; O. V. Kamlovskii. The sum of modules of Walsh coefficients of Boolean functions. Diskretnaya Matematika, Tome 27 (2015) no. 4, pp. 49-66. http://geodesic.mathdoc.fr/item/DM_2015_27_4_a4/