Decomposition of polynomials using the shift-composition operation
Abstract
V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.
Note
Originally published in Diskretnaya Matematika (2021) 33,№4, 68–82 (in Russian).
Dedicated to
the memory of Alexey Sergeevich Kuz’min
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On the existence of special nonlinear invariants for round functions of XSL-ciphers
- Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants
- Decomposition of polynomials using the shift-composition operation
- Mutually Orthogonal Latin Squares as Group Transversals
- Explicit basis for admissible rules in K-saturated tabular logics
- Criteria for maximal nonlinearity of a function over a finite field
Artikel in diesem Heft
- Frontmatter
- On the existence of special nonlinear invariants for round functions of XSL-ciphers
- Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants
- Decomposition of polynomials using the shift-composition operation
- Mutually Orthogonal Latin Squares as Group Transversals
- Explicit basis for admissible rules in K-saturated tabular logics
- Criteria for maximal nonlinearity of a function over a finite field
