On the period length of pseudorandom vector sequences generated by matrix generators
Jürgen Eichenauer‐Herrmann, Holger Grothe, Jürgen Lehn · Mathematics of Computation · 1989
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 {p^r} - 1 for any nonzero starting vector in case of a prime modulus p . For a modulus of the form p α {p^\alpha } , α ≥ 2 \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 ) ⋅ p α − 1 ({p^r} - 1) \cdot {p^{\alpha - 1}} for any starting vector which is nonzero modulo p .