The structure and enumeration of periodic binary sequences with high nonlinear complexity
Information Theory
2026-02-03 v1 math.IT
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.
Keywords
Cite
@article{arxiv.2602.01134,
title = {The structure and enumeration of periodic binary sequences with high nonlinear complexity},
author = {Qin Yuan and Chunlei Li and Xiangyong Zeng},
journal= {arXiv preprint arXiv:2602.01134},
year = {2026}
}