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设p为素数且正整数q|(p-1).本文利用剩余类环Zpm构造q-阶广义割圆分类,定义周期为pm的q元广义割圆序列,推广了已有文献中关于二元广义割圆序列的构造,并确定了当q为奇素数与q=4时该类序列的线性复杂度.结果表明,该类序列的线性复杂度大于周期的一半,能抗击应用Berlekamp-Massey算法的安全攻击.同时,应用类似的构造方法,提出了周期为pm的p元广义割圆序列,并预测了该序列的线性复杂度的具体取值.
Let p be a prime number and a positive integer q | (p-1). In this paper, we construct a q-generalized circumcircle classification using the remaining class ring Zpm and define a q-ary generalized circumscribed circle with a period of pm, And the linear complexity of the sequence is proved when q is an odd prime number and q = 4. The results show that the linear complexity of this kind of sequence is more than half of the period, which can resist the Berlekamp-Massey Algorithm.At the same time, by applying a similar construction method, a p-p generalized arc-cut sequence with a period of pm is proposed and the specific value of the linear complexity of the sequence is predicted.