中文摘要：

构造具有大线性复杂度和大集合容量的p元低相关序列集对码分多址（CDMA）通信系统具有重要的意义。采用Klapper的方法,利用d-型函数,构造了一类具有大集合容量的p元低相关序列集S（r）。该序列集的集合容量为p2n,序列的周期为p n-1,相关函数的最大边峰值为4 p n2-1。利用Key的方法,证明了当p=3或p=5该序列集的最小和最大线性复杂度分别为2n2-2n和3n2-1×2n2-2n;而当p〉5时,证明了其线性复杂度的最大和最小值分别大于3n4-1×2n4-2n和2n4-2n。该序列集能极大地提高CDMA通信系统的安全性。

英文摘要：

Constructing a large family of p-ary sequences with large linear complexity and low correlation is very important for code division multiple access（CDMA） communication systems.By use of Klapper’s method and d-form function,a large family S（r） of p-ary sequences with low correlation is constructed.Such family contains p 2n sequences of period pn-1 with maximal nontrivial correlation value 4 21np -.The minimal and maximal linear complexity of the sequences family are proven to be 2n2 -2n and 3n2-1 × 2n2-2n for p5 and r=（pm-1-1）/（p-1）,respectively.It is also proven that the maximal and minimal linearcomplexity of the sequences set are larger than 3n4-1 × 2n4-2n and 2n4-2n for p = 3,5 and r =（pm-1-1）/（p- 1）,respectively.This sequences family can greatly improve the security of CDMA communication systems.