On the linear disjunctive decomposition of a p-logic function into a product of functions
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Aleksandr V. Cheremushkin
Abstract
Let p be a prime number, p ≥ 3. We consider the set of decompositions of a p-logic function into a product of functions with disjoint subsets of variables obtained by means of linear substitutions of arguments. Each decomposition of this kind is associated with a decomposition of the vector space into a direct sum of subspaces. We present conditions under which such space decomposition is unique up to rearrangement of subspaces. Also, a criterion for such product to be balanced is given.
Originally published in Diskretnaya Matematika (2021) 33, №4, 153–171 (in Russian).
References
Cheremushkin A. V., “Uniqueness of product disjunctive decomposition of Boolean function to nonlinear irreducible factors”, Vestnik Mosk. gos. un-ta lesa «Lesnoy vestnik», 4(35) (2004), 186–190 (in Russian).Suche in Google Scholar
Marcus M., Minc H., A Survey of Matrix Theory and Matrix Inequalities, Allyn & Bacon, Inc., Boston, 1964.Suche in Google Scholar
Davis P. J., Circulant Matrices., 2nd ed., Chelsea, New York, 1994.Suche in Google Scholar
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Artikel in diesem Heft
- Frontmatter
- On the linear disjunctive decomposition of a p-logic function into a product of functions
- Hadamard square of linear codes and the generalized minimal distance of Reed–Muller code of order 2
-
Adapted spectral-differential method for construction of differentially 4-uniform piecewise-linear permutations, orthomorphisms, and involutions of the field
Artikel in diesem Heft
- Frontmatter
- On the linear disjunctive decomposition of a p-logic function into a product of functions
- Hadamard square of linear codes and the generalized minimal distance of Reed–Muller code of order 2
-
Adapted spectral-differential method for construction of differentially 4-uniform piecewise-linear permutations, orthomorphisms, and involutions of the field
