Abstract
The nonlinear complexity of binary sequences and its connections with Lempel-Ziv complexity is studied in this paper. A new recursive algorithm is presented, which produces the minimal nonlinear feedback shift register of a given binary sequence. Moreover, it is shown that the eigenvalue profile of a sequence uniquely determines its nonlinear complexity profile, thus establishing a connection between Lempel-Ziv complexity and nonlinear complexity. Furthermore, a lower bound for the Lempel-Ziv compression ratio of a given sequence is proved that depends on its nonlinear complexity.
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