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Piecewise polynomial sequences over the Galois ring

A. R. Vasin

Limited Liability Company “Certification Research Center,” Moscow, Russia

Abstract: We describe the construction of a piecewise polynomial generator over a Galois ring and prove a transitivity criterion for it. We give an estimate for the discrepancy of the output sequences of such a generator. We show that the obtained estimate is asymptotically equivalent to known estimates for special cases of a piecewise polynomial generator, and in some cases it is asymptotically sharper.

Keywords: piecewise polynomial sequences, Galois ring, distribution of elements in a sequence, discrepancy, exponential sums.

UDC: 621.391.1 : 519.7

Received: 21.07.2019
Revised: 05.02.2020
Accepted: 07.02.2020

DOI: 10.31857/S0555292320010088

 English version: Problems of Information Transmission, 2020, 56:1, 91–102

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