Applicable Algebra in Engineering, Communication and Computing

, Volume 10, Issue 3, pp 189-202

First online:

On the Distribution of Pseudorandom Numbers and Vectors Generated by Inversive Methods

  • Harald NiederreiterAffiliated withInstitute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria (e-mail:
  • , Igor E. ShparlinskiAffiliated withDepartment of Computing, Macquarie University, NSW 2109, Australia (e-mail:

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Inversive methods provide an attractive alternative to linear methods for pseudorandom number and vector generation. We present the first nontrivial results on the distribution of sequences of digital inversive pseudorandom numbers and inversive pseudorandom vectors in parts of the period. The proofs are based on a new bound for certain exponential sums over finite fields.

Keywords: Digital inversive pseudorandom numbers, Inversive pseudorandom vectors, Discrepancy, Exponential sums.