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Journal of Software:2012.23(4):952-961

一类本原σ-LFSR 序列的构造与计数
谭刚敏,曾光,韩文报,刘向辉
(解放军信息工程大学 信息工程学院, 河南 郑州 450002;解放军信息工程大学 信息工程学院, 河南 郑州 450002; 中国科学院 软件研究所 信息安全国家重点实验室, 北京 100190)
Construction and Enumeration of a Class of Primitive σ-LFSR Sequences
TAN Gang-Min,ZENG Guang,HAN Wen-Bao,LIU Xiang-Hui
(Institute of Information Engineering, PLA Information Engineering University, Zhengzhou 450002, China;Institute of Information Engineering, PLA Information Engineering University, Zhengzhou 450002, China; State Key Laboratory of Information Security, Institute of Software, The Chinese Academy of Sciences, Beijing 100190, China)
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Received:January 24, 2010    Revised:October 11, 2010
> 中文摘要: 有限域GF(2k)上本原σ-LFSR 序列的分量序列均是二元域上具有相同极小多项式的m-序列,已知一条GF(2k)上本原σ-LFSR 序列的距离向量,就可以用二元域上的m-序列构造它.研究了一类本原σ-LFSR 序列——Z 本原σ-LFSR 序列距离向量的计算问题.给出了一种GF(2k)上n 级Z 本原σ-LFSR 序列距离向量的计算方法,其主要思想是,利用GF(2k)上1 级Z 本原σ-LFSR 序列的距离向量来计算n 级Z 本原σ-LFSR 序列的距离向量.与其他现有方法相比,该方法的效率更高.更有价值的是,该方法也适用于GF(2k)上nm-序列距离向量的计算.最后给出了GF(2k)上n 级Z 本原σ-LFSR 序列的计数公式,说明其个数比GF(2k)上nm-序列更多.
Abstract:The coordinate sequences of a primitive σ-LFSR sequence over GF(2k) are m-sequences with the same minimal polynomial over GF(2), thus a primitive σ-LFSR sequence over GF(2k) can be constructed by m-sequences over GF(2) if its interval vector is known. This paper studies the calculation of interval vectors of a class of primitive σ-LFSR sequences—Z primitive σ-LFSR sequences and presents an improved method to calculate the interval vectors of Z primitive σ-LFSR sequences in order n over GF(2k), which uses the interval vectors of Z primitive σ-LFSR sequences of order 1 to calculate that of Z primitive σ-LFSR sequences in order n over GF(2k). In addition, it is more effective than other existing methods. More importantly, the new method can also be applied to the calculation of interval vectors of m-sequences over GF(2k). The enumeration formula of Z primitive σ-LFSR sequences of order n over GF(2k) is also presented, which shows that the number of Z primitive σ-LFSR sequences of order n is much larger than the number of m-sequences of order n over GF(2k).
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基金项目:国家自然科学基金(61003291); 国家高技术研究发展计划(863)(2009AA01Z417); 新世纪优秀人才计划(NCET-07-0384); 全国优秀博士学位论文作者专项基金(FANEDD-2007B74) 国家自然科学基金(61003291); 国家高技术研究发展计划(863)(2009AA01Z417); 新世纪优秀人才计划(NCET-07-0384); 全国优秀博士学位论文作者专项基金(FANEDD-2007B74)
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谭刚敏,曾光,韩文报,刘向辉.一类本原σ-LFSR 序列的构造与计数.软件学报,2012,23(4):952-961

TAN Gang-Min,ZENG Guang,HAN Wen-Bao,LIU Xiang-Hui.Construction and Enumeration of a Class of Primitive σ-LFSR Sequences.Journal of Software,2012,23(4):952-961