Linear Complexity of Generalized Cyclotomic Sequences with Period pm
Du Xiao-ni①②; Yan Tong-jiang③; Shi Yong-fang④
①College of Mathematic and Information Science, Northwest Normal University, Lanzhou 730070, China; ②State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing 100049, China; ③Institute of Mathematics and Computer Science, China University of Petroleum, Dongying 257061, China;④(College of Mathematic and Information Science, Gansu Lianhe University, Lanzhou 730070, China ④College of Mathematic and Information Science, Gansu Lianhe University, Lanzhou 730070, China
Abstract：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 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.
杜小妮; 阎统江; 石永芳. 周期为pm的广义割圆序列的线性复杂度[J]. 电子与信息学报, 2010, 32(4): 821-824 .
Du Xiao-ni①②; Yan Tong-jiang③; Shi Yong-fang④. Linear Complexity of Generalized Cyclotomic Sequences with Period pm. , 2010, 32(4): 821-824 .
2010, Vol. 32 
