Further Investigations on Nonlinear Complexity of Periodic Binary Sequences
Qin Yuan, Chunlei Li, Xiangyong Zeng, Tor Helleseth, Debiao He · IEEE Transactions on Information Theory · 2024
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit relation between nonlinear complexities of finite-length binary sequences and their corresponding periodic sequences. Based on the relation, we propose two algorithms that can generate all periodic binary sequences with any prescribed nonlinear complexity.