Matrices and the structure of random number sequences
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The rank R of the M x Q random binary matrix takes values r = 0,1,...,m where m = min{M,Q} with specified probabilities.
“The result states that the rank R of the M X Q random binary matrix takes values r = 0, 1, 2, . . . , m where m = min{M, Q) with probabihties ^2r{Q+M-r)-MQ jQ 1 (l-2^-«)(l-2^-^) i=0 1-2^”
From A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) · cites this paper as Marsaglia and Tsay (1985)
The rank test is based on the result of Kovalenko (1972) and also formulated in Marsaglia and Tsay (1985).
“It is based on the result of Kovalenko (1972) and also formulated in Marsaglia and Tsay (1985).”
From A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) · cites this paper as Marsaglia and Tsay (1985)
Cited by
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Bassham, L. E., Rukhin, A. L., Soto, J., Nechvatal, J. R., Smid, M. E., Barker, E. B., Leigh, S. D., Levenson, M., Vangel, M., Banks, D. L., et al. (2010) · NIST Special Publication 800-22 Revision 1a · doi:10.6028/nist.sp.800-22r1a · Cited by 3,617 · see citing works
Rukhin, A., Sota, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., et al. (2000) · doi:10.6028/nist.sp.800-22 · Cited by 1,867 · see citing works
Algorithm 806: SPRNG: a scalable library for pseudorandom number generation
Mascagni, M., & Srinivasan, A. (2000) · ACM Transactions on Mathematical Software · doi:10.1145/358407.358427 · Cited by 275 · see citing works
- Authors
- Marsaglia, G., & Tsay, L.-H.
- Affiliations
- Washington State University (US)
- Venue
- Linear Algebra and its Applications
- Publisher
- Elsevier BV
- Published
- 1985-06
- Volume
- 67
- Pages
- 147-156
- ISSN
- 0024-3795 (ISSN-L)
- OpenAlex
- W2030269782
- Cited by
- 118
- References
- 0
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 2 · 2023: 3 · 2022: 4 · 2021: 3 · 2020: 2 · 2019: 4 · 2018: 2 · 2017: 1 · 2016: 2 · 2015: 4 · 2014: 1 · 2013: 4 · 2012: 3
- FWCI
- 2.22
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Linear Algebra and its Applications (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Keywords
- random number generators, lagged Fibonacci generator, maximal period, linear recurrence sequences, matrix theory, linear algebra, starting values, pseudorandom sequences
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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