非线性反馈移位寄存器(NFSR)序列研究是密码学中重要的研究方向之一。De Bruijn序列是一类特殊的NFSR序列，由于具有良好的伪随机性质，在通信、密码学、生物信息等领域中有广泛的应用。本项目将利用多种数学工具对de Bruijn序列进行系统研究：研究快速生成高阶de Bruijn序列和大de Bruijn序列集的新方法；分析de Bruijn序列的线性复杂度、自相关和互相关性质。同时深入研究de Bruijn序列在如下两个领域中的应用：在通信领域中，研究可用于扩频通信的de Bruijn序列的构造；在生物信息领域中，继续研究de Bruijn序列在基于DNA的数据存储中的应用。该项目的研究将极大促进NFSR序列的研究进展，为建立安全的流密码体制提供重要的选择，为安全通信系统提供更多的性质优良的信号序列，并解决基于DNA的数据存储中的码率、编码方案等基本问题。

Studying sequences generated by Nonlinear Feedback Shift Registers (NFSRs) is an important research direction in cryptography. A special class of NFSR sequences is the class of de Bruijn sequences with good pseudorandomness. It has extensive applications in many domains such as communication, cryptography, and bioinformatics. This project aims to systematically study de Bruijn sequences using various mathematical tools. The main objective is to propose new construction methods capable of efficiently generating de Bruijn sequences in very large numbers and for larger orders. We also plan to analyze the linear complexity as well as the auto- and cross-correlation properties of the sequences. We will look into emerging applications of such sequences, especially in two domains. First, in communications, we will scrutinize their possible deployment in spread spectrum and construct spreading sequences from de Bruijn sequences. Second, in bioinformatics, the usefulness of de Bruijn and derived sequences in DNA-based data storage has recently been shown. We intend to continue our investigation along this topic. The above motivations strengthen our resolve to investigate NFSR sequences. We believe that at the end of this project we would be able to provide important parameter choices in the design of secure stream ciphers，produce more sequences with desirable properties for secure communication systems, and to solve some basic problems in DNA-based data storage such as determining the information rates and efficient encoding schemes.