Lattice computations for random numbers

Couture, Raymond; L’Ecuyer, Pierre

doi:10.1090/S0025-5718-99-01112-6

Lattice computations for random numbers
HTML articles powered by AMS MathViewer

by Raymond Couture and Pierre L’Ecuyer;

Math. Comp. 69 (2000), 757-765

DOI: https://doi.org/10.1090/S0025-5718-99-01112-6

Published electronically: February 24, 1999

PDF | Request permission

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

Raymond Couture, Pierre L’Ecuyer, and Shu 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 1176708, DOI 10.1090/S0025-5718-1993-1176708-4
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.
J. R. Heringa, H. W. J. Blöte, and A. Compagner, New primitive trinomials of Mersenne-exponent degrees for random-number generation, Internat. J. Modern Phys. C 3 (1992), no. 3, 561–564. MR 1169571, DOI 10.1142/S0129183192000361
Pierre L’Ecuyer, Maximally equidistributed combined Tausworthe generators, Math. Comp. 65 (1996), no. 213, 203–213. MR 1325871, DOI 10.1090/S0025-5718-96-00696-5
A. K. Lenstra, Factoring multivariate polynomials over finite fields, J. Comput. System Sci. 30 (1985), no. 2, 235–248. MR 801825, DOI 10.1016/0022-0000(85)90016-9
Leonard Eugene Dickson, New First Course in the Theory of Equations, John Wiley & Sons, Inc., New York, 1939. MR 2
Shu Tezuka, The $k$-dimensional distribution of combined GFSR sequences, Math. Comp. 62 (1994), no. 206, 809–817. MR 1223233, DOI 10.1090/S0025-5718-1994-1223233-9