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On the number of irreducible linear transformation shift registers
Jiang, Yupeng1; Yang, Jiangshuai2
2017-05-01
Source PublicationDESIGNS CODES AND CRYPTOGRAPHY
ISSN0925-1022
Volume83Issue:2Pages:445-454
AbstractWe deal with the problem of counting the number of irreducible linear transformation shift registers (TSRs) over a finite field. In a recent paper, Ram reduced this problem to calculate the cardinality of some set of irreducible polynomials and got explicit formulae for the number of irreducible TSRs of order two. We find a bijection between Ram's set to another set of irreducible polynomials which is easier to count, and then give a conjecture about the number of irreducible TSRs of any order. We also get explicit formulae for the number of irreducible TSRs of order three.
KeywordLinear feedback shift register Transformation shift register Irreducible polynomial Mobius inversion formula
DOI10.1007/s10623-016-0240-5
Language英语
Funding ProjectNational Natural Science Foundation of China[61379139] ; National Natural Science Foundation of China[61502483] ; National Natural Science Foundation of China[11526215] ; Chinese Academy of Sciences[XDA06010701]
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000396812200010
PublisherSPRINGER
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25172
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, NCMIS, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Jiang, Yupeng,Yang, Jiangshuai. On the number of irreducible linear transformation shift registers[J]. DESIGNS CODES AND CRYPTOGRAPHY,2017,83(2):445-454.
APA Jiang, Yupeng,&Yang, Jiangshuai.(2017).On the number of irreducible linear transformation shift registers.DESIGNS CODES AND CRYPTOGRAPHY,83(2),445-454.
MLA Jiang, Yupeng,et al."On the number of irreducible linear transformation shift registers".DESIGNS CODES AND CRYPTOGRAPHY 83.2(2017):445-454.
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