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. 
@article{PDM_2016_1_a3,
     author = {A. V. Cheremushkin},
     title = {On linear decomposition of {Boolean} functions},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {46--56},
     publisher = {mathdoc},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2016_1_a3/}
}
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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/