Tausworthe, R. C. 1965. Random numbers generated by linear recurrence modulo two . The maximal period of 2 k Gamma 1 and can be achieved using as few as two non zero values of a i . This leads to a very fast random number generator. While these two methods seem different, they are very related, and theoretical results for one always hold for the other.
Serious correlations can result if k is small.
The shift register sequences can be parameterized through the choice of a i . This is to be expected as the full period of the LMG produces all possible k tuples modulo m. For dimensions larger than k, behavior analogous to the LCG in two or more dimensions is seen. Shift Register Generators. While these two methods seem different, they are very related, and theoretical results for one always hold for the other.