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| 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 |
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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.
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Received: 30 March 2009
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Corresponding Authors:
Du Xiao-ni
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2010, Vol. 32 
