A Generalization of Shift-Register Sequence Generators

Abstract

Abstract : The paper examines the questions 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 X sub n 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 m(2 raised to the n power) for any m and n by cyclic application of properly chosen transformations. (Author)