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

Eichenauer-Herrmann, Jürgen; Grothe, Holger; Lehn, Jürgen

doi:10.1090/S0025-5718-1989-0946603-0

On the period length of pseudorandom vector sequences generated by matrix generators
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by Jürgen Eichenauer-Herrmann, Holger Grothe and Jürgen Lehn PDF

Math. Comp. 52 (1989), 145-148 Request permission

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.

References

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Contribution aux Générateurs de Vecteurs Pseudo-Aléatoires