Geodesic
On linear decomposition of Boolean functions
Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 46-56
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Disjunctive decompositions of Boolean functions taken after a linear substitution on the set of arguments are considered. For any component of such a decomposition, a notion of a substantial variables subspace is introduced. The main topic of the article is to give some sufficient condition under which the both these subspaces unequally determine each other in a simple disjunctive decomposition of a function having the trivial stabiliser group of shifts. The case of iterative disjunctive decomposition is considered too.
Keywords: Boolean function, vector space, dual space, simple disjunctive decomposition, iterative disjunctive decomposition. 
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     author = {A. V. Cheremushkin},
     title = {On linear decomposition of {Boolean} functions},
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A. V. Cheremushkin. On linear decomposition of Boolean functions. Prikladnaâ diskretnaâ matematika, no. 1 (2016), pp. 46-56. http://geodesic.mathdoc.fr/item/PDM_2016_1_a3/

[1] Cheremushkin A. V., “Methods of affine and linear classification of binary functions”, Tr. Diskr. Mat., 4, 2001, 273–314 (in Russian)

[2] Cheremushkin A. V., “The uniqueness of the binary function decomposition in a unrepeated product of non-linear irreducible factors”, Lesnoy vestnik, 2004, no. 4(35), 86–90 (in Russian)