Remarks on nonlinear congruential pseudorandom numbers
type: Item
instance of: scholarly article
title: Remarks on nonlinear congruential pseudorandom numbers
zbMATH Open document ID: 0663.65005
DOI: 10.1007/BF02613320
author: Harald Niederreiter
published in: Metrika
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176198
review text: Let \(x_ 1,x_ 2,...,x_ n,..\). be a sequence of pseudorandom numbers obtained by a generator producing a permutation of \(\{\) 1,2,...,p\(\}\), p a prime. Let \(u_ n=(0,x_{n+1}-x_ n,x_{n+2}-x_ n,...,x_{n+p- 1}-x_ n)\) and \(G^{(d)}\) be the \(d\times p\) matrix with rows \(u_ 0,u_ 1,...,u_{d-1}\). We say that the generator passes the d- dimensional lattice test iff rank \((G^{(d)})=d\). Consider the generator \(x_{n+1}=ax_ n+b\), where \(\bar O=O\), \(\bar c=c^{-1}\) (in the field \(F_ p)\). If this generator has period p then it passes the lattice test for all \(d\leq (p+1)/2\). Some generalizations of the result for the fields \(F_ q\) where q is some power of a prime \(p\geq 3\) are given.
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 4084825
zbMATH Keywords: pseudorandom numbers
zbMATH Keywords: nonlinear congruential method
zbMATH Keywords: lattice test
zbMATH Keywords: linear recurring sequence
zbMATH Keywords: permutation polynomial
reviewed by: Jaroslav Král
MaRDI profile type: Publication
cites work: Marsaglia's lattice test and non-linear congruential pseudo-random number generators
cites work: Q3746773
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cites work: Equidistribution of linear recurring sequences in finite fields, II
OpenAlex ID: W2076887562
description: scientific article; zbMATH DE number 4084825