A wide family of nonlinear filter functions with a large linear span

Authors:
P. Caballero-Gil;A. Fúster-Sabater
Affiliations:
DEIOC, University of La Laguna, 38271 La Laguna, Tenerife, Spain;DTIC, Insitute of Applied Physics, CSIC, CISerrano 144, 28006 Madrid, Spain
Venue:
Information Sciences—Informatics and Computer Science: An International Journal
Year:
2004

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Abstract

A broad collection of pseudorandom sequence generators is introduced. These generators are based on nonlinear functions applied to maximal-length LFSRs and are not constrained in the length L of the LFSRs or the nonlinear order k of the functions. The linear span of the resulting sequences is proved to be as large as the linear span of the sequences obtained from a product of equidistant phases, that is to say, at Least (Lk). A count of the number of functions is evaluated and compared with the corresponding count of products of equidistant phases.