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| construction and enumeration of a class of primitive σ-lfsr sequences | |
| Alternative Title | Construction and Enumeration of a Class of Primitive σ-LFSR Sequences |
| Tan Gang-Min; Zeng Guang; Han Wen-Bao; Liu Xiang-Hui | |
| 2012 | |
| Source | Ruan Jian Xue Bao/Journal of Software
 |
| ISSN | 10009825 |
| Volume | 23Issue:4Pages:952-961 |
| 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. |
| 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. |
| Keyword | Binary Sequences |
| 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 |
| Language | 中文 |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/14625 |
| Collection | 信息安全国家重点实验室 |
| Recommended Citation 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. |
| Files in This Item: | ||||||
| File Name/Size | DocType | Version | Access | License | ||
| 一类本原σ-LFSR序列的构造与计数.p（1157KB） | 开放获取 | License | Application Full Text | |||
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