Likelihood that a pseudorandom sequence generator has optimal properties

TL;DR

This paper proves that as the length of the linear feedback shift register increases, the probability of randomly selecting a nonlinear filter with optimal properties approaches certainty.

Contribution

It establishes an asymptotic probability result showing that randomly chosen nonlinear filters are almost surely optimal for large shift register lengths.

Findings

Probability tends to 1 for optimal properties as register length increases

Maximum period and linear complexity are highly likely in large nonlinear filters

Supports the effectiveness of random selection in designing optimal sequences

Abstract

The authors prove that the probability of choosing a nonlinear filter of m-sequences with optimal properties, that is, maximum period and maximum linear complexity, tends assymptotically to 1 as the linear feedback shift register length increases.