Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Lattice computations for random numbers


Authors: Raymond Couture and Pierre L'Ecuyer
Journal: Math. Comp. 69 (2000), 757-765
MSC (1991): Primary 65C10
DOI: https://doi.org/10.1090/S0025-5718-99-01112-6
Published electronically: February 24, 1999
MathSciNet review: 1651748
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We improve on a lattice algorithm of Tezuka for the computation of the $k$-distribution of a class of random number generators based on finite fields. We show how this is applied to the problem of constructing, for such generators, an output mapping yielding optimal $k$-distribution.


References [Enhancements On Off] (What's this?)

  • 1. R. Couture, P. L'Ecuyer, and S. Tezuka, On the distribution of $k$-dimensional vectors for simple and combined Tausworthe sequences, Math. Comp. 60 (1993), no. 202, 749-761, S11-S16. MR 93h:11085
  • 2. M. Fushimi and S. Tezuka, The $k$-distribution of generalized feedback shift register pseudorandom numbers, Communications of the ACM 26 (1983), no. 7, 516-523.
  • 3. J. R. Heringa, H. W. J. Blöte, and A. Compagner, New primitive trinomials of Mersenne-exponent degrees for random-number generation, Internat. J. of Modern Phys. C 3 (1992), no. 3, 561-564. MR 94a:11118
  • 4. P. L'Ecuyer, Maximally equidistributed combined Tausworthe generators, Math. Comp. 65 (1996), no. 213, 203-213. MR 96d:65017
  • 5. A. K. Lenstra, Factoring multivariate polynomials over finite fields, J. Comput. System Sci. 30 (1985), 235-248. MR 87a:11124
  • 6. K. Mahler, An analogue to Minkowski's geometry of numbers in a field of series, Ann. of Math. 42 (1941), no. 2, 488-522. MR 2:350c
  • 7. S. Tezuka, The $k$-dimensional distribution of combined GFSR sequences, Math. Comp. 62 (1994), no. 206, 809-817. MR 94i:65014

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (1991): 65C10

Retrieve articles in all journals with MSC (1991): 65C10


Additional Information

Raymond Couture
Affiliation: Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email: couture@iro.umontreal.ca

Pierre L'Ecuyer
Affiliation: Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada
Email: lecuyer@iro.umontreal.ca

DOI: https://doi.org/10.1090/S0025-5718-99-01112-6
Keywords: Random number generation, lattice structure
Received by editor(s): April 7, 1998
Received by editor(s) in revised form: July 24, 1998
Published electronically: February 24, 1999
Additional Notes: This work has been supported by NSERC-Canada grants no. OGP0110050 and SMF0169893 to the second author.
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society