Abstract:
We study the class of functions defined on a finite field GF(q)GF(q) and constructed by means of linear recurrent sequences over the Galois ring GR(qn,pn)GR(qn,pn). 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.
\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{https://elibrary.ru/item.asp?id=37652151}
Linking options:
https://www.mathnet.ru/eng/mvk268
https://doi.org/10.4213/mvk268
https://www.mathnet.ru/eng/mvk/v9/i4/p31
This publication is cited in the following 5 articles:
O. V. Kamlovskii, K. N. Pankov, “Klass diskretnykh funktsii, postroennykh po neskolkim lineinym rekurrentam nad primarnym koltsom vychetov”, Diskret. matem., 37:1 (2025), 9–21
A. D. Bugrov, O. V. Kamlovskii, “Svoistva klassov bulevykh funktsii, postroennykh iz neskolkikh lineinykh rekurrent nad koltsom vychetov Z2n”, Matem. vopr. kriptogr., 15:4 (2024), 9–22
A. A. Gruba, “Bulevy funktsii, postroennye po razryadnym posledovatelnostyam lineinykh rekurrent”, Diskret. matem., 35:1 (2023), 54–61
A. D. Bugrov, “Svoistva klassov bulevykh funktsii, postroennykh iz neskolkikh lineinykh rekurrent nad koltsom vychetov Z2n”, PDM. Prilozhenie, 2023, no. 16, 12–14
O. V. Kamlovskii, V. V. Mizerov, “Kross-korrelyatsionnaya funktsiya predstavlenii odnogo klassa posledovatelnostei nad koltsami Galua”, Matem. vopr. kriptogr., 14:4 (2023), 71–88
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