On the linear disjunctive decomposition of a p-logic function into a sum 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 sum 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.
Originally published in Diskretnaya Matematika (2022) 34, №4, 99–107 (in Russian).
References
1 Cheremushkin A. V., “On the linear disjunctive decomposition of a p-logic function into a product of functions”. Discrete Math. Appl. 35:1 (2025), 1–14.10.1515/dma-2025-0001Search in Google Scholar
2 Cheremushkin A. V., “The condition for uniqueness of decomposition into a sum of functions under a linear change of variables”, Prikladnaya diskretnaya matematika. Prilozhenie 10 (2017), 55–56 (in Russian).Search in Google Scholar
3 Cheremushkin A. V., “On the linear decomposition of binary functions”, Prikladnaya diskretnaya matematika 40:2 (2018), 10-22 (in Russian).Search in Google Scholar
4 Cheremushkin A. V., “Additive approach to the determining the nonlinearity degree of a discrete function”, Prikladnaya diskretnaya matematika 8:2 (2010), 22–33 (in Russian).10.17223/20710410/8/4Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation
Articles in the same Issue
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation
