Geodesic
The Spectral Test of the Boolean Function Linearity
International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) no. 4, pp. 567-575

Voir la notice de l'article provenant de la source Library of Science

The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be performed by means of other methods. In particular, the basic synthesis method described in the paper allows us to compute the spectral coefficients in an iterative manner. The method can be easily used in investigations of large Boolean functions (of many variables), which seems very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.
Keywords: Walsh coefficients, coefficient distribution, Boolean function, bent functions, linearity measure of a Boolean function
Mots-clés : informatyka 
@article{IJAMCS_2003_13_4_a12,
     author = {Porwik, P.},
     title = {The {Spectral} {Test} of the {Boolean} {Function} {Linearity}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {567--575},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_4_a12/}
}
TY  - JOUR
AU  - Porwik, P.
TI  - The Spectral Test of the Boolean Function Linearity
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2003
SP  - 567
EP  - 575
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_4_a12/
LA  - en
ID  - IJAMCS_2003_13_4_a12
ER  - 
%0 Journal Article
%A Porwik, P.
%T The Spectral Test of the Boolean Function Linearity
%J International Journal of Applied Mathematics and Computer Science
%D 2003
%P 567-575
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_4_a12/
%G en
%F IJAMCS_2003_13_4_a12
Porwik, P. The Spectral Test of the Boolean Function Linearity. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) no. 4, pp. 567-575. http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_4_a12/