A Wide Family of Nonlinear Filter Functions with a Large Linear Span

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 . A count of the number of functions is evaluated and compared with the corresponding count of products of equidistant phases.