中文摘要：

Helleseth-Gong（HG）序列是一类具有理想自相关性的无线通信系统码分多址（CDMA）序列.对奇素数p和整数n,m,d满足n=（2d＋1）m,本文利用有限域上的二次型理论和迹变换的性质在HG序列基础上构造一类序列数目众多,具有最佳相关性的非平衡p元CDMA序列族,其最佳相关性用Welch下界来衡量.同样,对偶数n=2（2d＋1）m,在改进非平衡p元CDMA序列族基础上利用有限域上的迹变换构造了一类序列数目众多,具有最佳相关性的平衡p元CDMA序列族.文章证明了这两类CDMA序列族中的序列都具有大的周期与线性复杂度,适合在无线通信信道上传输.

英文摘要：

The Helleseth-Gong （HG） sequence is a kind of CDMA sequences used in wireless communication systems with ideal autocorrelation. For an odd prime p and integers n, m, d satisfying n = （2d ＋ 1 ） m, using the theory of quadratic forms and properties of trace transform over finite field, a new unbalanced p-ary CDMA sequence family with large family size and optimal correlation property is constructed based on HG sequences, which means the family has optimal correlation in terms of Welch＇ s lower bound. Similarly, for an even number n = 2 （2 d ＋ 1 ） m, using the trace transform, a family of balanced p-ary CDMA sequences with large family size has the property of optimal correlation, which is constructed from the unbalanced p-ary CDMA sequence family. It is shown that the two CDMA sequence families have large period and linear span, and are suitable for transmission in wireless communication systems.