周期为pm的广义割圆序列的线性复杂度

杜小妮; 阎统江; 石永芳

doi:10.3724/SP.J.1146.2009.00430

周期为pm的广义割圆序列的线性复杂度

doi: 10.3724/SP.J.1146.2009.00430

杜小妮^{①②;阎统江,},
阎统江,
石永芳

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出版历程
- 收稿日期: 2009-03-30
- 修回日期: 2009-10-19
- 刊出日期: 2010-04-19

Linear Complexity of Generalized Cyclotomic Sequences with Period pm

Du Xiao-ni^{①②;阎统江
,},
Yan Tong-jiang,
Shi Yong-fang

摘要

摘要: 该文将周期为pm(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pm-1, pm,(pm-1)/2和(pm+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。
- 流密码; 广义割圆序列; 线性复杂度; 极小多项式
Abstract: In this paper, a new class of generalized cyclotomic sequences of period pm(p odd prime and m1) 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 pm-1, pm, (pm-1)/2 and (pm+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.

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参考文献(1)

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