construction and enumeration of a class of primitive &sigma;-lfsr sequences

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	construction and enumeration of a class of primitive σ-lfsr sequences
	Tan Gang-Min ; Zeng Guang ; Han Wen-Bao ; Liu Xiang-Hui
刊名	Ruan Jian Xue Bao/Journal of Software
	2012
卷号	23 期号:4 页码:952-961
关键词	流密码本原σ-LFSR m-序列距离向量线性复杂度计数
ISSN号	1000-9825
其他题名	Construction and Enumeration of a Class of Primitive σ-LFSR Sequences
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n级m-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n级m-序列更多.
英文摘要	The coordinate sequences of a primitive σ-LFSR sequence over GF(2^k) are m-sequences with the same minimal polynomial over GF(2), thus a primitive σ-LFSR sequence over GF(2^k) 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(2^k), 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(2^k). 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(2^k). The enumeration formula of Z primitive σ-LFSR sequences of order n over GF(2^k) 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(2^k). © 2012 ISCAS.
收录类别	EI ; CNKI ; WANFANG
资助信息	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)
语种	中文
公开日期	2013-09-17
内容类型	期刊论文
源URL	[http://ir.iscas.ac.cn/handle/311060/14909]
专题	软件研究所_软件所图书馆_期刊论文
推荐引用方式 GB/T 7714	Tan Gang-Min,Zeng Guang,Han Wen-Bao,et al. construction and enumeration of a class of primitive σ-lfsr sequences[J]. Ruan Jian Xue Bao/Journal of Software,2012,23(4):952-961.
APA	Tan Gang-Min,Zeng Guang,Han Wen-Bao,&Liu Xiang-Hui.(2012).construction and enumeration of a class of primitive σ-lfsr sequences.Ruan Jian Xue Bao/Journal of Software,23(4),952-961.
MLA	Tan Gang-Min,et al."construction and enumeration of a class of primitive σ-lfsr sequences".Ruan Jian Xue Bao/Journal of Software 23.4(2012):952-961.