d-元广义分圆序列的线性复杂度及自相关函数性质分析

Analysis of the Linear Complexity and the Autocorrelation of a Class of d-ary Generalized Cyclotomic Sequence

该文推广了Liu Fang等人(2010)给出的周期为p n,p为奇素数,n为正整数的广义分圆序列的构造,并确定了新构造序列的线性复杂度和自相关函数值的分布。结果表明,推广的构造保持了原构造的高线性复杂度等伪随机特性。由于取值更灵活,较之原构造新构造序列的数量要大得多。

The construction of the generalized cyclotomic sequence with length pn for a prime p and a positive integer n given by Liu Fang et al. （2010） is generalized in this paper. The linear complexity and the autocorrelation values of the new defined sequences are also determined. The results show that the new defined sequences keep the pseudo-random properties of the original sequence, that is, the high linear complexity and undesirable autocorrelation properties. Owing to the flexible ways to assign values to different generalized cyclotomic classes, the new construction contains more classes of generalized cyclotomic sequences when it is compared with the original one.