Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles

Feedback shift registers can be applied to the fields of communications, stream ciphers, computers, and design theory. The linear feedback shift registers are often used in the construction of De Bruijn sequences. For any given linear shift register, its cycle structure and adjacency graphs are feat...

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Main Authors:	Xiaofang Wang, Linzhi Jiang
Format:	Article
Language:	English
Published:	IEEE 2018-01-01
Series:	IEEE Access
Subjects:	Cycle structure adjacency graph cyclotomy number De Bruijn cycle
Online Access:	https://ieeexplore.ieee.org/document/8408786/

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record_format	Article
spelling	doaj-12f5489368f54bdfa09f7ad789f9b2ea2021-03-29T20:43:31ZengIEEEIEEE Access2169-35362018-01-016387703877910.1109/ACCESS.2018.28542658408786Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn CyclesXiaofang Wang0https://orcid.org/0000-0002-8488-1559Linzhi Jiang1State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, ChinaSchool of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, ChinaFeedback shift registers can be applied to the fields of communications, stream ciphers, computers, and design theory. The linear feedback shift registers are often used in the construction of De Bruijn sequences. For any given linear shift register, its cycle structure and adjacency graphs are features that must be investigated in the construction of the De Bruijn sequences by using the cycle-joining method. A class of linear feedback shift registers is discussed in this paper. The cycle structure of some linear feedback shift registers is derived. And the adjacency graphs are divided into two categories to analyze their structure in detail. Based on this kind of linear feedback shift registers combined with the cycle-joining method, a novel family of De Bruijn cycles is obtained. The number of the corresponding De Bruijn cycles produced is also proposed exactly.https://ieeexplore.ieee.org/document/8408786/Cycle structureadjacency graphcyclotomy numberDe Bruijn cycle
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Xiaofang Wang Linzhi Jiang
spellingShingle	Xiaofang Wang Linzhi Jiang Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles IEEE Access Cycle structure adjacency graph cyclotomy number De Bruijn cycle
author_facet	Xiaofang Wang Linzhi Jiang
author_sort	Xiaofang Wang
title	Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles
title_short	Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles
title_full	Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles
title_fullStr	Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles
title_full_unstemmed	Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles
title_sort	cycle structure and adjacency graphs of a class of lfsrs and a new family of de bruijn cycles
publisher	IEEE
series	IEEE Access
issn	2169-3536
publishDate	2018-01-01
description	Feedback shift registers can be applied to the fields of communications, stream ciphers, computers, and design theory. The linear feedback shift registers are often used in the construction of De Bruijn sequences. For any given linear shift register, its cycle structure and adjacency graphs are features that must be investigated in the construction of the De Bruijn sequences by using the cycle-joining method. A class of linear feedback shift registers is discussed in this paper. The cycle structure of some linear feedback shift registers is derived. And the adjacency graphs are divided into two categories to analyze their structure in detail. Based on this kind of linear feedback shift registers combined with the cycle-joining method, a novel family of De Bruijn cycles is obtained. The number of the corresponding De Bruijn cycles produced is also proposed exactly.
topic	Cycle structure adjacency graph cyclotomy number De Bruijn cycle
url	https://ieeexplore.ieee.org/document/8408786/
work_keys_str_mv	AT xiaofangwang cyclestructureandadjacencygraphsofaclassoflfsrsandanewfamilyofdebruijncycles AT linzhijiang cyclestructureandadjacencygraphsofaclassoflfsrsandanewfamilyofdebruijncycles
_version_	1724194220313411584

Cycle Structure and Adjacency Graphs of a Class of LFSRs and a New Family of De Bruijn Cycles

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