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

In Tahmi [5], Niederreiter [41, Afflerbach and Grothe [1], and Grothe [21 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 pr 1 for any nonzero starting vector in case of a prime modulus p. For a modulus of the form pa, a > 2 and p prime, this paper describes a simple method for constructing matrix generators having the maximal possible period length (pr 1) p'-1 for any starting vector which is nonzero modulo p.