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Theoretical Foundations of Applied Discrete Mathematics
Digit-polynomial construction of substitutions over Galois ring
M. V. Zaets Research Institute "Kvant", Moscow
Abstract:
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.
Keywords:
substitutions, $n$-quasigroups, bijective polynomial vector-function, functions with variational-digit polynomiality, digit set, Galois ring.
Citation:
M. V. Zaets, “Digit-polynomial construction of substitutions over Galois ring”, Prikl. Diskr. Mat. Suppl., 2017, no. 10, 17–19
Linking options:
https://www.mathnet.ru/eng/pdma369 https://www.mathnet.ru/eng/pdma/y2017/i10/p17
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