Research and Advances

The k-distribution of generalized feedback shift register pseudorandom numbers

Posted

A necessary and sufficient condition is established for the generalized feedback shift register (GFSR) sequence introduced by Lewis and Payne to be k-distributed. Based upon the theorem, a theoretical test for k-distributivity is proposed and performed in a reasonable amount of computer time, even for k = 16 and a high degree of resolution (for which statistical tests are impossible because of the astronomical amount of computer time required). For the special class of GFSR generators considered by Arvillias and Maritsas based on the primitive trinomial Dp + Dq + 1 with q = an integral power of 2, it is shown that the sequence is k-distributed if and only if the lengths of all subregisters are at least k. The theorem also leads to a simple and efficient method of initializing the GFSR generator so that the sequence to be generated is k-distributed.

View this article in the ACM Digital Library.

Join the Discussion (0)

Become a Member or Sign In to Post a Comment

The Latest from CACM

Shape the Future of Computing

ACM encourages its members to take a direct hand in shaping the future of the association. There are more ways than ever to get involved.

Get Involved

Communications of the ACM (CACM) is now a fully Open Access publication.

By opening CACM to the world, we hope to increase engagement among the broader computer science community and encourage non-members to discover the rich resources ACM has to offer.

Learn More