KMS Of Academy of mathematics and systems sciences, CAS
On the number of irreducible linear transformation shift registers | |
Jiang, Yupeng1; Yang, Jiangshuai2 | |
2017-05-01 | |
发表期刊 | DESIGNS CODES AND CRYPTOGRAPHY |
ISSN | 0925-1022 |
卷号 | 83期号:2页码:445-454 |
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. |
关键词 | Linear feedback shift register Transformation shift register Irreducible polynomial Mobius inversion formula |
DOI | 10.1007/s10623-016-0240-5 |
语种 | 英语 |
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 |
WOS类目 | Computer Science, Theory & Methods ; Mathematics, Applied |
WOS记录号 | WOS:000396812200010 |
出版者 | SPRINGER |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/25172 |
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. |
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