Matrices and the structure of random number sequences (Q1062414)

This paper discusses the maximum period and randomness structure of two random number generators: shift-register and lagged-Fibonacci. Two theorems on the period of the random number generators are derived using linear algebra and matrix theory. Some regularities of m-tuples of points are shown for the shift-register generators analogous to that for the congruential random number generators. It is also suggested that no such regularities are appeared for the lagged-Fibonacci generators since lags are long enough.