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arXiv · 2602.01134

The structure and enumeration of periodic binary sequences with high nonlinear complexity

Qin Yuan·Chunlei Li·Xiangyong Zeng
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Abstract

Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary sequences with nonlinear complexity larger than or equal to 3n/4 is characterized. Based on their structure, an exact enumeration formula for the number of such periodic sequences is determined.

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Qin Yuan, Chunlei Li, Xiangyong Zeng. 2026-02-01. The structure and enumeration of periodic binary sequences with high nonlinear complexity. https://arxiv.org/abs/2602.01134

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