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On the number of irreducible linear transformation shift registers

文献类型：期刊论文

作者Jiang, Yupeng1; Yang, Jiangshuai2
刊名DESIGNS CODES AND CRYPTOGRAPHY
出版日期2017-05-01
卷号83期号:2页码:445-454
关键词Linear feedback shift register Transformation shift register Irreducible polynomial Mobius inversion formula
ISSN号0925-1022
DOI10.1007/s10623-016-0240-5
英文摘要We 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.
资助项目National 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研究方向Computer Science ; Mathematics
语种英语
WOS记录号WOS:000396812200010
出版者SPRINGER
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/25171]  
专题中国科学院数学与系统科学研究院
通讯作者Jiang, Yupeng
作者单位1.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
推荐引用方式
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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