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.

翻译：非线性复杂度是评估序列随机性的重要指标。本文研究了循环移位对有限长二元序列非线性复杂度的影响，进而揭示了有限长二元序列与其对应周期序列之间更明确的非线性复杂度关系。基于该关系，我们提出了两种算法，可生成任意指定非线性复杂度的全部周期二元序列。