Cover: A Generalization of Shift Register Sequence Generators

A Generalization of Shift Register Sequence Generators

Published 1969

by I. S. Reed, Rein Turn

Purchase Print Copy

 Format Price
Add to Cart Paperback37 pages $20.00

This paper examines the question of the existence and the design of feedback shift-register sequence generators (FSR) capable of producing sequences with periods longer than obtained by the classical linear or nonlinear feedback shift-register techniques. This capability is achieved by cyclically modifying the effective connections in the feedback loop. A description of the behavior of the classical n-stage FSR in terms of cyclic transformations on its state space, represented by n-tuples of x, is formulated and used to analyze the behavior of the proposed generalized n-stage feedback shift-register, the (m,n)-FSR. The latter is shown to be capable of producing sequences of maximal period as the product m2 with a variable exponent n for any m and n by cyclic application of properly chosen transformations. (See also P-3473.)

This report is part of the RAND paper series. The paper was a product of RAND from 1948 to 2003 that captured speeches, memorials, and derivative research, usually prepared on authors' own time and meant to be the scholarly or scientific contribution of individual authors to their professional fields. Papers were less formal than reports and did not require rigorous peer review.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit

RAND is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.