An additive congruential method for generating a multiple occurrence uniform random sequence

Abstract

The formalism behind a novel additive congruential method (ACM) is described. This method yields uniform random sequences whose outcomes occur more than once throughout the sequence. The approach to generating a uniformly distributed pseudorandom sequence (PS) is presented. For a selected prime, p, the PS is a sequence of random variables (RV) over the Galois field GF(p). The ACM yields a Markov PS, where each valid outcome appears more than once within the main period, and still obeys a uniform distribution.