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- Makoto Matsumoto, Yoshiharu Kurita
- ACM Trans. Model. Comput. Simul.
- 1994

The twisted GFSR generators proposed in a previous article have a defect in <italic>k</italic>-distribution for <italic>k</italic> larger than the order of recurrence. In this follow up article, we introduce and analyze a new TGFSR variant having better <italic>k</italic>-distribution property. We provide an efficient algorithm to obtain the order of… (More)

- Makoto Matsumoto, Yoshiharu Kurita
- ACM Trans. Model. Comput. Simul.
- 1992

The generalized feed back shift register (GFSR) algorithm suggested by Lewis and Payne is a widely used pseudorandom number generator, but has the following serious drawbacks: (1) an initialization scheme to assure higher order equidistribution is involved and is time consuming; (2) each bit of the generated words constitutes an <italic>m</italic>-sequence… (More)

- Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, Makoto Matsumoto
- Math. Comput.
- 2000

All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X859433 +X288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

- Makoto Matsumoto, Yoshiharu Kurita
- TOMC
- 1996

The fixed vector of any <italic>m</italic>-sequence based on a trinomial is explicitly obtained. Local nonrandomness around the fixed vector is analyzed through model-construction and experiments. We conclude that the initial vector near the fixed vector should be avoided.

- Makoto Matsumoto, Yoshiharu Kurita
- ACM Trans. Model. Comput. Simul.
- 1996

- MERSENNE EXPONENT, Toshihiro Kumada, Hannes Leeb, Yoshiharu Kurita, Makoto Matsumoto
- 2000

All primitive trinomials over GF (2) with degree 859433 (which is the 33rd Mersenne exponent) are presented. They are X859433 +X288477 + 1 and its reciprocal. Also two examples of primitive pentanomials over GF (2) with degree 86243 (which is the 28th Mersenne exponent) are presented. The sieve used is briefly described.

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