Title: construction and enumeration of a class of primitive σ-lfsr sequences
Alternative Title: Construction and Enumeration of a Class of Primitive σ-LFSR Sequences
Author: Tan Gang-Min
; Zeng Guang
; Han Wen-Bao
; Liu Xiang-Hui
Keyword: Binary sequences
Source: Ruan Jian Xue Bao/Journal of Software
Issued Date: 2012
Volume: 23, Issue: 4, Pages: 952-961 Department: (1) Institute of Information Engineering, PLA Information Engineering University, Zhengzhou 450002, China; (2) State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
Abstract: 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. English 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 ). © 2012 ISCAS. Language: 中文
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/14625
Appears in Collections: 信息安全国家重点实验室_期刊论文
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Recommended Citation:
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,2012-01-01,23(4):952-961.
