Period-Different m-Sequences With at Most Four-Valued Cross Correlation

doi:10.1109/TIT.2009.2021312

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	Period-Different m-Sequences With at Most Four-Valued Cross Correlation
	Helleseth, Tor 1; Hu, Lei 2,3; Kholosha, Alexander 1; Zeng, Xiangyong 4; Li, Nian 4; Jiang, Wenfeng 3
	2009-07-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	55 期号:7 页码:3305-3311
摘要	This paper follows the recent work of Helleseth, Kholosha, Johansen, and Ness to study the cross correlation between an m.-sequence of period 2(m) - 1 and the d-decimation of an in-sequence of a shorter period 2(n) - 1 for an even number m = 2n. Assuming that d satisfies d(2(l) + 1) = 2(i) (mod 2(n) - 1) for some l > 0 and i >= 0, it is proved that the cross correlation takes on either exactly three or four values depending on whether l and n are coprime or not. The distribution of the cross-correlation values is also completely determined. Our results theoretically confirm the numerical data by Ness and Helleseth. It is conjectured that there are no other decimations that give at most four-valued cross correlation apart from the ones proved here.
关键词	Cross correlation m-sequence quadratic form
DOI	10.1109/TIT.2009.2021312
语种	英语
资助项目	National Science Foundation of China (NSFC)[60573053] ; National Science Foundation of China (NSFC)[60773134] ; NSFC[60603012]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000267222000026
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8636
专题	中国科学院数学与系统科学研究院
通讯作者	Helleseth, Tor
作者单位	1.Univ Bergen, Dept Informat, N-5020 Bergen, Norway 2.Chinese Acad Sci, AMSS, Inst Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Grad Univ, State Key Lab Informat Secur, Beijing 100049, Peoples R China 4.Hubei Univ, Fac Math & Comp Sci, Wuhan 430062, Peoples R China
推荐引用方式 GB/T 7714	Helleseth, Tor,Hu, Lei,Kholosha, Alexander,et al. Period-Different m-Sequences With at Most Four-Valued Cross Correlation[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2009,55(7):3305-3311.
APA	Helleseth, Tor,Hu, Lei,Kholosha, Alexander,Zeng, Xiangyong,Li, Nian,&Jiang, Wenfeng.(2009).Period-Different m-Sequences With at Most Four-Valued Cross Correlation.IEEE TRANSACTIONS ON INFORMATION THEORY,55(7),3305-3311.
MLA	Helleseth, Tor,et al."Period-Different m-Sequences With at Most Four-Valued Cross Correlation".IEEE TRANSACTIONS ON INFORMATION THEORY 55.7(2009):3305-3311.