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

Harald Niederreiter; Arne Winterhof

Acta Arithmetica (2000)

  • Volume: 93, Issue: 4, page 387-399
  • ISSN: 0065-1036

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Harald Niederreiter, and Arne Winterhof. "Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators." Acta Arithmetica 93.4 (2000): 387-399. <http://eudml.org/doc/207421>.

@article{HaraldNiederreiter2000,
author = {Harald Niederreiter, Arne Winterhof},
journal = {Acta Arithmetica},
keywords = {finite field; upper bounds; exponential sum; sequences of digital explicit inversive pseudorandom numbers; explicit inversive pseudorandom vectors},
language = {eng},
number = {4},
pages = {387-399},
title = {Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators},
url = {http://eudml.org/doc/207421},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Harald Niederreiter
AU - Arne Winterhof
TI - Incomplete exponential sums over finite fields and their applications to new inversive pseudorandom number generators
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 4
SP - 387
EP - 399
LA - eng
KW - finite field; upper bounds; exponential sum; sequences of digital explicit inversive pseudorandom numbers; explicit inversive pseudorandom vectors
UR - http://eudml.org/doc/207421
ER -

References

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  1. [1] T. Cochrane, On a trigonometric inequality of Vinogradov, J. Number Theory 27 (1987), 9-16. Zbl0629.10030
  2. [2] J. Eichenauer-Herrmann, Statistical independence of a new class of inversive congruential pseudorandom numbers, Math. Comp. 60 (1993), 375-384. Zbl0795.65002
  3. [3] P. Hellekalek, General discrepancy estimates: the Walsh function system, Acta Arith. 67 (1994), 209-218. Zbl0805.11055
  4. [4] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed., Cambridge Univ. Press, Cambridge, 1994. Zbl0820.11072
  5. [5] C. J. Moreno and O. Moreno, Exponential sums and Goppa codes: I, Proc. Amer. Math. Soc. 111 (1991), 523-531. Zbl0716.94010
  6. [6] H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, SIAM, Philadelphia, 1992. 
  7. [7] H. Niederreiter, Pseudorandom vector generation by the inversive method, ACM Trans. Modeling and Computer Simulation 4 (1994), 191-212. Zbl0847.11039
  8. [8] H. Niederreiter, Improved bounds in the multiple-recursive matrix method for pseudorandom number and vector generation, Finite Fields Appl. 2 (1996), 225-240. Zbl0893.11031
  9. [9] H. Niederreiter and I. E. Shparlinski, On the distribution of inversive congruential pseudorandom numbers in parts of the period, Math. Comp., to appear. Zbl0983.11048
  10. [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. Zbl0942.11037
  11. [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. Zbl0999.11040
  12. [12] A. Winterhof, On the distribution of powers in finite fields, Finite Fields Appl. 4 (1998), 43-54. Zbl0910.11055

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