Inversive congruential generator over a Galois ring of dimension p~l

摘要

We consider the construction of of an inversive congruential generator over a Galois ring of odd dimension p~l, which was proposed by Sole and Zinoviev for p = 2. Using the estimates of trigonometric sums on the sequences of pseudorandom numbers, we obtain the estimates of a discrepant function, a generated sequence of pseudorandom numbers, and the associated sequence of two-dimensional "overlapping" points.