Geodesic
Approximation of restrictions of $q$-valued logic functions to linear manifolds by affine analogues
Diskretnaya Matematika, Tome 32 (2020) no. 4, pp. 89-102

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For a finite $q$-element field $\mathbf{F}_q$, 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 $q^{n-1}(q-1) - q^{n/2-1}$ and $q^{r-1}(q - 1) - q^{r/2-1}$, 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.
Keywords: $q$-valued logic, restriction, manifold, affine function, nonlinearity. 
@article{DM_2020_32_4_a4,
     author = {V. G. Ryabov},
     title = {Approximation of restrictions of $q$-valued logic functions to linear manifolds by affine analogues},
     journal = {Diskretnaya Matematika},
     pages = {89--102},
     publisher = {mathdoc},
     volume = {32},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_4_a4/}
}
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V. G. Ryabov. Approximation of restrictions of $q$-valued logic functions to linear manifolds by affine analogues. Diskretnaya Matematika, Tome 32 (2020) no. 4, pp. 89-102. http://geodesic.mathdoc.fr/item/DM_2020_32_4_a4/