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Journal of Computational and Applied Mathematics - Random numbers and simulation
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ACM Transactions on Modeling and Computer Simulation (TOMACS)
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Some linear and nonlinear methods for pseudorandom number generation
WSC '95 Proceedings of the 27th conference on Winter simulation
Uniform random number generators: a review
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Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Uniform random number generators
Proceedings of the 30th conference on Winter simulation
Tables of 64-bit Mersenne twisters
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the xorshift random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Designs, Codes and Cryptography
Quasi-cyclic codes as codes over rings of matrices
Finite Fields and Their Applications
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SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
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Designs, Codes and Cryptography
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We carry out an in-depth analysis of the multiple-recursive matrix method for uniform pseudorandom number generation which was introduced in an earlier paper of the author. This method yields much larger period lengths than the GFSR method with the same order of the recursion and the same precision. Besides periodicity properties, we establish also uniformity properties of s-tuples of successive pseudorandom numbers generated by the multiple-recursive matrix method and we study the performance under the s-dimensional serial test. The uniformity properties and the behavior under the serial test depend on an appropriate figure of merit in the case where the dimension s exceeds the order of the recursion.