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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - R. A. De La Krus Khimenes
AU  - O. V. Kamlovskii
TI  - The sum of modules of Walsh coefficients of Boolean functions
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 49
EP  - 66
VL  - 27
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_4_a4/
LA  - ru
ID  - DM_2015_27_4_a4
ER  - 
%0 Journal Article
%A R. A. De La Krus Khimenes
%A O. V. Kamlovskii
%T The sum of modules of Walsh coefficients of Boolean functions
%J Diskretnaya Matematika
%D 2015
%P 49-66
%V 27
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_4_a4/
%G ru
%F DM_2015_27_4_a4
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/

[1] Logachev O.A., Salnikov A.A., Smyshlyaev S.V., Yaschenko V.V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2012, 584 pp.

[2] Kamlovskii O.V., “Kolichestvo poyavlenii elementov v vykhodnykh posledovatelnostyakh filtruyuschikh generatorov”, Prikladnaya diskretnaya matematika, 2013, no. 3(21), 11–25

[3] McFarland R.L., “A family of difference sets in non-cyclic groups”, J. Comb. Theory. Ser. A, 15:1 (1973), 1–10 | DOI | MR | Zbl

[4] Carlet C., “A large class of cryptographic Boolean functions via a study of the Maiorana–McFarland construction”, Lect. Notes Comput. Sci., 2442 (2002), 549–564 | DOI | MR | Zbl

[5] Dobbertin H., “Construction of bent functions and balanced Boolean functions with high nonlinearity”, Lect. Notes Comput. Sci., 1008 (1995), 61–74 | DOI | Zbl

[6] Glukhov M.M., Elizarov V.P., Nechaev A.A., Algebra, Uchebnik, Gelios ARV, M., 2003, 416 pp.

[7] Riordan D., Kombinatornye tozhdestva, Nauka, M., 1982, 256 pp. | MR

[8] Rueppel R.A., Analysis and design of stream ciphers, Springer-Verlag, 1986, 244 pp. | MR | Zbl

[9] Carlet C., “Boolean functions for cryptography and error correcting codes”, Boolean Models and Methods in Mathematics, Computer Science, and Engineering, eds. Y. Crama, P. L. Hammer, Cambridge Univ. Press, 2010, 257–397 | DOI | Zbl