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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The serial test for a nonlinear pseudorandom number generator


Authors: Takashi Kato, Li-Ming Wu and Niro Yanagihara
Journal: Math. Comp. 65 (1996), 761-769
MSC (1991): Primary 65C10; Secondary 11K45
MathSciNet review: 1333317
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Abstract: Let $M = 2^{w},$ and $G_{M} = \{1,3,...,M-1 \}.$ A sequence $ \{y_{n} \}, y_{n} \in G_{M},$ is obtained by the formula $y_{n+1} \equiv a{\overline{y}_{n}} + b + cy_{n} \; \mathrm{mod} \; M.$ The sequence $ \{x_{n} \}, x_{n}=y_{n}/M,$ is a sequence of pseudorandom numbers of the maximal period length $M/2$ if and only if $a+c \equiv 1$ (mod 4), $b \equiv 2$ (mod 4). In this note, the uniformity is investigated by the 2-dimensional serial test for the sequence. We follow closely the method of papers by Eichenauer-Herrmann and Niederreiter.


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Additional Information

Takashi Kato
Affiliation: Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan

Li-Ming Wu
Affiliation: Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan

Niro Yanagihara
Affiliation: Department of Mathematics, Faculty of Science, Chiba University, 1-33 Yayoi-cho, Chiba City, 263 Japan
Email: yanagi@math.s.chiba-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00712-0
PII: S 0025-5718(96)00712-0
Keywords: Pseudorandom number generator, the inversive congruential method, power of two modulus, discrepancy, $k$-dimensional serial test, Kloostermann sum
Received by editor(s): October 25, 1994
Article copyright: © Copyright 1996 American Mathematical Society