Gold序列互相关性的新证明及非最大Gold序列性质研究  

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

作　　者：王玉东[1] 刘春雷[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《通信技术》2014年第3期241-246,共6页Communications Technology

基　　金：国家自然科学基金(No.11071160)~~

摘　　要：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。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.

关 键 词：伪随机序列 GOLD序列 自相关性 互相关性 

分 类 号：TN911[电子电信—通信与信息系统] O15[电子电信—信息与通信工程]