Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators

• Autorzy: Harald Niederreiter , Arne Winterhof
• Języki publikacji: EN

Kategorie tematyczne

• 65C10: Random number generation
• 11K38: Irregularities of distribution, discrepancy
• 11T23: Exponential sums
• 11K45: Pseudo-random numbers; Monte Carlo methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 4
• Strony: 387-399

Daty

wydano

2000

otrzymano

1999-12-03

Twórcy

autor

Harald Niederreiter

• Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Wien, Austria

autor

Arne Winterhof

• Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Wien, Austria

Bibliografia

• [1] T. Cochrane, On a trigonometric inequality of Vinogradov, J. Number Theory 27 (1987), 9-16.
• [2] J. Eichenauer-Herrmann, Statistical independence of a new class of inversive congruential pseudorandom numbers, Math. Comp. 60 (1993), 375-384.
• [3] P. Hellekalek, General discrepancy estimates: the Walsh function system, Acta Arith. 67 (1994), 209-218.
• [4] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge Univ. Press, Cambridge, 1994.
• [5] C. J. Moreno and O. Moreno, Exponential sums and Goppa codes: I, Proc. Amer. Math. Soc. 111 (1991), 523-531.
• [6] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992.
• [7] H. Niederreiter, Pseudorandom vector generation by the inversive method, ACM Trans. Modeling and Computer Simulation 4 (1994), 191-212.
• [8] H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225-240.
• [9] H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, Math. Comp., to appear.
• [10] H. Niederreiter and I. E. Shparlinski, On the distribution and lattice structure of nonlinear congruential pseudorandom numbers, Finite Fields Appl. 5 (1999), 246-253.
• [11] H. Niederreiter and I. E. Shparlinski, On the distribution of pseudorandom numbers and vectors generated by inversive methods, Appl. Algebra Engrg. Comm. Comput., to appear.
• [12] A. Winterhof, On the distribution of powers in finite fields, Finite Fields Appl. 4 (1998), 43-54.