Geodesic
Digit-polynomial construction of substitutions over Galois ring
Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 17-19.

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A new way for constructing substitutions over Galois ring is considered. The way uses functions with variational-digit polynomiality. The class of these functions over various rings was earlier defined in the author's works. The peculiarity of this class is that it contains a class of polynomial functions and, under certain conditions, does not coincide with it. The criterions for the bijectivity of a polynomial vector-function and for a polynomial function to be a substitution are generalized. The presented results make it possible, in particular, to construct non-polynomial $n$-quasigroups.
Mots-clés : substitutions
Keywords: $n$-quasigroups, bijective polynomial vector-function, functions with variational-digit polynomiality, digit set, Galois ring. 
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     title = {Digit-polynomial construction of substitutions over {Galois} ring},
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M. V. Zaets. Digit-polynomial construction of substitutions over Galois ring. Prikladnaya Diskretnaya Matematika. Supplement, no. 10 (2017), pp. 17-19. http://geodesic.mathdoc.fr/item/PDMA_2017_10_a4/

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