Gold序列互相关性的新证明及非最大Gold序列性质研究

Gold序列是通信中常用的伪随机序列。提供了一种Gold序列自相关性和互相关性的新的证明，不同于Kasami早先的用循环码理论的证明，本证明直接从Gold序列的定义出发，应用了有限域上迹函数性质和指数和的理论，比原证明更直观、简洁，并且直接推广到了非互素采样的情形---非最大Gold序列。随后讨论了非最大Gold序列的自相关性和互相关性，发现这时的相关函数取值为五值的，具有一定的应用价值。

A New proof of Cross-Correlation Property of Gold Sequence and Non-Maximal Gold Sequence

Gold sequence is the pseudo-noise sequence commonly used in communication technology. A new proof of the autocorrelation and cross-correlation property of Gold sequence is proposed. Unlike the o-riginal cyclic codes proof of Kasami, the proposed proof is directly started from the definition of Gold se-quence. The theory of finite fields and exponential sums is used, this makes the proof more intuitive and explicit. Then the proof is generalized to the case of non-prime decimation,called non-maximal Gold se-quence. It is found that the autocorrelation and cross-correlation functions of non-maximal Gold sequence are five-valued, thus having some important application value.