On the lattice structure of a nonlinear generator with modulus \(2^{\alpha}\)
type: Item
instance of: scholarly article
title: On the lattice structure of a nonlinear generator with modulus \(2^{\alpha}\)
zbMATH Open document ID: 0702.65006
DOI: 10.1016/0377-0427(90)90338-Z
author: Jürgen Eichenauer-Herrmann
author: Holger Grothe
author: Harald Niederreiter
author: Alev Topuzoğlu
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let \(Z_ m=\{0,1,...,m-1\}\), \(Z^*_{2^{\alpha}}=\{1,3,...,2^{\alpha}-1\}\) for m,\(\alpha\in N\). Define a nonlinear generator by \(x_{n+1}\equiv ax_ n^{-1}+b(mod 2^{\alpha})\) (1), \(n\geq 0\), where \(x^{-1}\) is the unique element in \(Z^*_{2^{\alpha}}\) with x \(x^{-1}\equiv 1 mod(2^{\alpha})\) for \(x\in Z^*_{2^{\alpha}}\) and \(x_ 0\in Z^*_{2^{\alpha}}\). Assumptions such that (1) has maximal period length \(2^{\alpha -1}\) are given. It is proved that the set of consecutive pseudorandom numbers forms a superposition of shifted lattices. The lattice bases are determined.
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 4151694
zbMATH Keywords: nonlinear pseudorandom numbers
zbMATH Keywords: lattice structure
zbMATH Keywords: superposition of shifted lattices
Wikidata QID: Q21725884
reviewed by: Wilfried Grecksch
MaRDI profile type: Publication
cites work: On the structure of quadratic congruential sequences
cites work: A Nonlinear Congruential Pseudorandom Number Generator with Power of Two Modulus
full work available at URL: 0377-0427(90)90338-z
OpenAlex ID: W2050104580
description: scientific article; zbMATH DE number 4151694