本项目将以有限域和编码的理论为工具，研究m序列与其采样序列之间以及不同采样序列之间的相关性. 已有结果主要处理的是二次的采样因子，本项目将重点研究非二次的. 在此基础上利用采样方法和移位相加的思想，来构造一批新的具有优异性能的低相关序列集.预期的研究成果将为密码系统和通信系统提供更多满足实际需求的序列集.

Utilizing the theory of finite fields and the coding theory, this project mainly investigates the cross-correlation properties between m-sequence and its decimated sequences, and the cross-correlation properties between different decimated sequences of m-sequene. The decimation factors of existing results almost are quadratic, while the decimation factors considered in this project are mainly non-quadratic. Furthermore, with these results about the correlation properties and the idea of shifts and addtions, some good sequence families with low correlation will be constructed. The obtained results will not only enrich the theory of sequence design but also provied more suitable sequence families for communication systems and cryptographic systems.