一类大集合p元低相关序列集的线性复杂度研究

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pn-1,相关函数的最大边峰值为4p(n)/(2)-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2(n)/(2)-2n和3(n)/(2)-1×2(n)/(2)-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3(n)/(4)-1×2(n)/(4)-2n和2(n)/(4)-2n。该序列集能极大地提高CDMA通信系统的安全性。

Research on the Linear Complexity for a Family of Large Size of p-ary Sequences with Low Correlation

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 p2n sequences of period pn-1 with maximal nontrivial correlation value 4p(n)/(2)-1. The minimal and maximal linear complexity of the sequences family are proven to be 2(n)/(2)-2n and 3(n)/(2)-1×2(n)/(2)-2n for p > 5 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 3(n)/(4)-1×2(n)/(4)-2n and 2(n)/(4)-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.