A Generalization of Shift Register Sequence Generators

by I. S. Reed, Rein Turn

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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.)

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