Approximation of restrictions of q-valued logic functions to linear manifolds by affine analogues
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Vladimir G. Ryabov
Abstract
For a finite q-element field Fq, we established a relation between parameters characterizing the measure of affine approximation of a q-valued logic function and similar parameters for its restrictions to linear manifolds. For q > 2, an analogue of the Parseval identity with respect to these parameters is proved, which implies the meaningful upper estimates qn−1(q − 1) − qn/2−1 and qr−1(q − 1) − qr/2−1, for the nonlinearity of an n-place q-valued logic function and of its restrictions to manifolds of dimension r. Estimates characterizing the distribution of nonlinearity on manifolds of fixed dimension are obtained.
Note: Originally published in Diskretnaya Matematika (2020) 32,№4, 89–102 (in Russian).
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Articles in the same Issue
- Frontmatter
- A method of construction of differentially 4-uniform permutations over Vm for even m
- Ergodicity of the probabilistic converter, a serial connection of two automata
- On distance-regular graphs with c2 = 2
- Minimal contact circuits for characteristic functions of spheres
- Approximation of restrictions of q-valued logic functions to linear manifolds by affine analogues
- Multiaffine polynomials over a finite field
- Large deviations of branching process in a random environment. II
Articles in the same Issue
- Frontmatter
- A method of construction of differentially 4-uniform permutations over Vm for even m
- Ergodicity of the probabilistic converter, a serial connection of two automata
- On distance-regular graphs with c2 = 2
- Minimal contact circuits for characteristic functions of spheres
- Approximation of restrictions of q-valued logic functions to linear manifolds by affine analogues
- Multiaffine polynomials over a finite field
- Large deviations of branching process in a random environment. II
