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Abstract.
It is shown that aq-periodic sequence over the finite fieldFq passes an extended version of Marsaglia's lattice test for high dimensions if and only if its linear complexity is large. The consequences of this result for nonlinear and inversive pseudorandom number generators are worked out.
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Linear complexity of a class of pseudorandom sequences over a general finite field
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Authors and Affiliations
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore (e-mail: nied@math.nus.edu.sg), , , , , , SG
Harald Niederreiter
Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, 1010 Vienna, Austria (e-mail: arne.winterhof@oeaw.ac.at), , , , , , AT
Arne Winterhof
- Harald Niederreiter
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- Arne Winterhof
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Received: October 2, 2001
Keywords: Pseudorandom number generator, Nonlinear method, Inversive method, Linear complexity, Marsaglia's lattice test.
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Niederreiter, H., Winterhof, A. Lattice Structure and Linear Complexity of Nonlinear Pseudorandom Numbers.AAECC13, 319–326 (2002). https://doi.org/10.1007/s002000200105
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