On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders

Frances Griffin; Harald Niederreiter; Igor E. Shparlinski

doi:10.1007/3-540-46796-3_9

On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders

Frances Griffin, Harald Niederreiter, Igor E. Shparlinski

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

24 Citations (Scopus)

Abstract

The nonlinear congruential method is an attractive alternative to the classical linear congruentialmethod for pseudorandom number generation. In this paper we present a new type of discrepancy bound for sequences of s-tuples of successive nonlinear multiple recursive congruential pseudorandom numbers of higher orders. In particular, we generalize some recent results about recursive congruential pseudorandom numbers of first order.

Original language	English
Title of host publication	Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Subtitle of host publication	13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings
Editors	Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli
Place of Publication	Berlin; New York
Publisher	Springer, Springer Nature
Pages	87-93
Number of pages	7
ISBN (Electronic)	9783540467960
ISBN (Print)	3540667237, 9783540667230
DOIs	https://doi.org/10.1007/3-540-46796-3_9
Publication status	Published - Nov 1999
Event	13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC - 1999 - Honolulu, United States Duration: 15 Nov 1999 → 19 Nov 1999

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	1719
ISSN (Print)	03029743
ISSN (Electronic)	16113349

Other

Other	13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC - 1999
Country/Territory	United States
City	Honolulu
Period	15/11/99 → 19/11/99

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10.1007/3-540-46796-3_9

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Griffin, F., Niederreiter, H., & Shparlinski, I. E. (1999). On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. In M. Fossorier, H. Imai, S. Lin, & A. Poli (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings (pp. 87-93). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1719). Springer, Springer Nature. https://doi.org/10.1007/3-540-46796-3_9

Griffin, Frances ; Niederreiter, Harald ; Shparlinski, Igor E. / On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings. editor / Marc Fossorier ; Hideki Imai ; Shu Lin ; Alain Poli. Berlin; New York : Springer, Springer Nature, 1999. pp. 87-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The nonlinear congruential method is an attractive alternative to the classical linear congruentialmethod for pseudorandom number generation. In this paper we present a new type of discrepancy bound for sequences of s-tuples of successive nonlinear multiple recursive congruential pseudorandom numbers of higher orders. In particular, we generalize some recent results about recursive congruential pseudorandom numbers of first order.",

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Griffin, F, Niederreiter, H & Shparlinski, IE 1999, On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. in M Fossorier, H Imai, S Lin & A Poli (eds), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1719, Springer, Springer Nature, Berlin; New York, pp. 87-93, 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC - 1999, Honolulu, Hawaii, United States, 15/11/99. https://doi.org/10.1007/3-540-46796-3_9

On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. / Griffin, Frances; Niederreiter, Harald; Shparlinski, Igor E.
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings. ed. / Marc Fossorier; Hideki Imai; Shu Lin; Alain Poli. Berlin; New York: Springer, Springer Nature, 1999. p. 87-93 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1719).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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N2 - The nonlinear congruential method is an attractive alternative to the classical linear congruentialmethod for pseudorandom number generation. In this paper we present a new type of discrepancy bound for sequences of s-tuples of successive nonlinear multiple recursive congruential pseudorandom numbers of higher orders. In particular, we generalize some recent results about recursive congruential pseudorandom numbers of first order.

AB - The nonlinear congruential method is an attractive alternative to the classical linear congruentialmethod for pseudorandom number generation. In this paper we present a new type of discrepancy bound for sequences of s-tuples of successive nonlinear multiple recursive congruential pseudorandom numbers of higher orders. In particular, we generalize some recent results about recursive congruential pseudorandom numbers of first order.

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Griffin F, Niederreiter H, Shparlinski IE. On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders. In Fossorier M, Imai H, Lin S, Poli A, editors, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings. Berlin; New York: Springer, Springer Nature. 1999. p. 87-93. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46796-3_9

On the distribution of nonlinear recursive congruential pseudorandom numbers of higher orders

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