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On the period length of pseudorandom vector sequences generated by matrix generators

Authors: Jürgen Eichenauer-Herrmann, Holger Grothe and Jürgen Lehn
Journal: Math. Comp. 52 (1989), 145-148
MSC: Primary 65C10; Secondary 11K45
MathSciNet review: 946603
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Abstract: In Tahmi [5], Niederreiter [4], Afflerbach and Grothe [1], and Grothe [2] linear recursive congruential matrix generators for generating r-dimensional pseudorandom vectors are analyzed. In particular, conditions are established which ensure that the period length equals $ {p^r} - 1$ for any nonzero starting vector in case of a prime modulus p. For a modulus of the form $ {p^\alpha }$, $ \alpha \geq 2$ and p prime, this paper describes a simple method for constructing matrix generators having the maximal possible period length $ ({p^r} - 1) \cdot {p^{\alpha - 1}}$ for any starting vector which is nonzero modulo p.

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  • [1] Lothar Afflerbach and Holger Grothe, The lattice structure of pseudo-random vectors generated by matrix generators, J. Comput. Appl. Math. 23 (1988), no. 1, 127–131. MR 952072, 10.1016/0377-0427(88)90338-X
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  • [3] Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878
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Keywords: Pseudorandom vector sequences, matrix generator, period length
Article copyright: © Copyright 1989 American Mathematical Society