English

Binary sequences with length n and nonlinear complexity not less than n/2

Information Theory 2023-12-27 v1 math.IT

Abstract

In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all binary sequences with length nn and nonlinear complexity cnn/2c_{n}\geq n/2, where nn is an integer larger than 22. Furthermore, a formula is established to calculate the exact number of these sequences. The distribution of nonlinear complexity for these sequences is thus completely determined.

Keywords

Cite

@article{arxiv.2108.11859,
  title  = {Binary sequences with length n and nonlinear complexity not less than n/2},
  author = {Sicheng Liang and Xiangyong Zeng and Zibi Xiao and Zhimin Sun},
  journal= {arXiv preprint arXiv:2108.11859},
  year   = {2023}
}