, Volume 39, Issue 2, pp 155–163 | Cite as

Optimal characteristic polynomials for digital multistep pseudorandom numbers

  • G. L. Mullen
  • H. Niederreiter
Contributed Papers


The digital multistep method generates uniform pseudorandom numbers by transforming sequences of integers obtained by multistep recursions. The statistical independence properties of these pseudorandom numbers depend on the characteristic polynomial of the recursion. We describe a method of calculating characteristic polynomials that are optimal with respect to statistical independence of pairs of successive pseudorandom numbers. Tables of such optimal characteristic polynomials for degrees ≤64 are included.

AMS Subject Classifications

Primary 65C10 secondary 11T06, 11Y65 

Key words

Uniform pseudorandom numbers digital multistep method serial test continued fractions for rational functions 

Optimale charakteristische Polynome für Pseudozufallszahlen nach der digitalen Mehrschrittmethode


Die digitale Mehrschrittmethode erzeugt gleichverteilte Pseudozufallszahlen durch Transformation von Folgen ganzer Zahlen, die aus Rekursionen höherer Ordnung gewonnen werden. Die statistischen Unabhängigkeitseigenschaften dieser Pseudozufallszahlen hängen vom charakteristischen Polynom der Rekursion ab. Es wird eine Methode zur Berechnung von charakteristischen Polynomen beschrieben, welche bezüglich der statistischen Unabhängigkeit von Paaren aufeinanderfolgender Pseudozufallszahlen optimal sind. Die Arbeit enthält auch Tabellen solcher optimaler charakteristischer Polynome für Grade ≤64.


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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • G. L. Mullen
    • 1
  • H. Niederreiter
    • 2
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.Mathematical InstituteAustrian Academy of SciencesViennaAustria

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