中文摘要：

该文将周期为p^m（p为奇素数,m为正整数）广义割圆的研究推广到了任意阶的情形,构造了一类新序列,确定了该序列的极小多项式,指出线性复杂度可能的取值为p^m-1,p^m,（p^m-1）/2和（p^m＋1）/2。并且指出,当选取的特征集满足一定条件时,对应序列的线性复杂度取值总是以上4种情形。结果表明,该类序列具有较好的线性复杂度性质。

英文摘要：

In this paper,a new class of generalized cyclotomic sequences of period pm（ p odd prime and m 1） with arbitrary order is constructed and its minimal polynomial is determined. Hence the linear complexity of it is obtained. The possible values of its linear complexity are pointed out,which is p^m-1,p^m,（ p^m-1）/2 and （ p^m＋ 1）/2. The research also indicate that linear complexity of the sequences always take the values as above when the corresponding characteristic sets satisfies certain conditions. The results show that most of these sequences have good linear complexity.