The k-distribution of generalized feedback shift register pseudorandom numbers

M. Fushimi, S. Tezuka

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)516-523
Number of pages8
JournalCommunications of the ACM
Volume26
Issue number7
DOIs
Publication statusPublished - Jul 1 1983

All Science Journal Classification (ASJC) codes

  • Computer Science(all)

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