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Mat. Vopr. Kriptogr., 2018, Volume 9, Issue 4, Pages 31–52 (Mi mvk268)  

Parameters of a class of functions over a finite field

A. D. Bugrov, O. V. Kamlovskii

Certification Research Center, LLC, Moscow

Abstract: We study the class of functions defined on a finite field $GF(q)$ and constructed by means of linear recurrent sequences over the Galois ring $GR(q^n, p^n)$. For this class we investigate: the distances between functions, the distance to the class of affine functions, the number of constructed functions and the number of preimages of elements under action of functions. It is shown that the functions are significantly distant from the class of all affine functions.

Key words: linear recurrent sequences, discrete functions, finite fields, Galois ring, cross-correlation function.

DOI: https://doi.org/10.4213/mvk268

Full text: PDF file (275 kB)
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UDC: 519.716.5+519.113.6
Received 18.IV.2018

Citation: A. D. Bugrov, O. V. Kamlovskii, “Parameters of a class of functions over a finite field”, Mat. Vopr. Kriptogr., 9:4 (2018), 31–52

Citation in format AMSBIB
\Bibitem{BugKam18}
\by A.~D.~Bugrov, O.~V.~Kamlovskii
\paper Parameters of a class of functions over a finite field
\jour Mat. Vopr. Kriptogr.
\yr 2018
\vol 9
\issue 4
\pages 31--52
\mathnet{http://mi.mathnet.ru/mvk268}
\crossref{https://doi.org/10.4213/mvk268}
\elib{http://elibrary.ru/item.asp?id=37652151}


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