On the number of irreducible linear transformation shift registers

doi:10.1007/s10623-016-0240-5

	On the number of irreducible linear transformation shift registers
	Jiang, Yupeng 1; Yang, Jiangshuai 2
刊名	DESIGNS CODES AND CRYPTOGRAPHY
	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
DOI	10.1007/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
出版者	SPRINGER
WOS记录号	WOS:000396812200010
内容类型	期刊论文
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.