CrossCorrelation Properties of Perfect Binary Sequences

doi:10.13190/jbupt.201002.78.272

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2010, Vol. 33 ›› Issue (2): 78-81.doi: 10.13190/jbupt.201002.78.272

• Reports • Previous Articles Next Articles

CrossCorrelation Properties of Perfect Binary Sequences

ZHUO Ze-peng1,2, XIAO Guo-zhen1

(1National Key Laboratory of Integrated Service Network, Xidian University, Xian 710071, China; 
2School of Mathematical Science, Huaibei Coal Industry Teachers College, Huaibei, Anhui 235000, China)

Received:2009-07-19 Revised:1900-01-01 Online:2010-04-28 Published:2010-04-28

Abstract

Abstract:

For odd n, the crosscorrelation function between a decimated DillonDobbertin (DD) sequence and WelchGong (WG) sequence is investigated, and the crosscorrelation function between a pair of Hyperoval sequences is studied. It is shown that the calculation of the crosscorrelation functions between a decimated DD sequence and WG sequence, and a pair of Hyperoval sequences could be reduced to the calculation of the crosscorrelation between msequences and their decimations. The crosscrrelation function between a decimated DD sequence and WG sequence could be 3valued under a 2^k+1decimation.

Key words: crosscorrelation function, perfect sequences, decimation, DillonDobbertin sequence, WelchGong sequence, Hyperoval sequence

CLC Number:

TN918.1

ZHUO Ze-peng, XIAO Guo-zhen. CrossCorrelation Properties of Perfect Binary Sequences[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2010, 33(2): 78-81.

References

[1] Jungnickel D, Pott A. Perfect and almost perfect sequences. Discrete Applied Mathmatics, 1999, 95(1-3): 331-359.
[2] Gordon B, Mills W H, Welch L R. Some new difference sets[J]. Canadian Journal of Mathematics, 1962, 14(4): 614-625.
[3] Dillon J F, Dobbertin H. New cyclic difference sets with singer parameters[J]. Finite Fields and Their Applications, 2004, 10(3): 342-389.
[4] No J S, Golomb S W, Gong G, et al. Binary pseudorandom sequences of period 2^m-1 with ideal autocorrelation[J]. IEEE Trans on Inform Theory, 1998, 44(2): 814-817.
[5] Maschietti A. Difference sets and hyperovals[J]. Designs, Codes and Cryptography, 1998, 14(1): 89-98.
[6] Gold R. Maximal recursive sequences with 3-valued recursive cross-correlation functions[J]. IEEE Trans Inform Theory, 1968(14): 154-156.
[7] Games R A. Cross-correlation of m-sequences and GMW-sequences with the same primitive polynomial[J]. Discrete Applied Mathematics, 1985, 12: 139-146.
[8] Antweiler M. Cross-correlation of p-ary GMW sequences[J]. IEEE Trans Inform Theory, 1994, 40(4): 1253-1261.
[9] Gong Guang, Golomb S W. The decimation-Hadamard transform of two-level auto-correlation sequences[J]. IEEE Trans Inform Theory, 2002, 48(4): 853-865.
[10] Yu Y N, Gong Guang. Cross-correlation properties of binary sequences with ideal two-level autocorrelation//Sequences and Their Applications (SETA 2006). : Springer-Verlag, 2006: 104-118.
[11] Dillon J F. Multiplicative difference sets via additive characters. Designs, Codes and Cryptography, 1999, 17(1-3): 225-235.
[12] Hertel D. Cross-correlation properties of perfect binary sequences//Sequences and Their Applications (SETA 2004). : Springer-Verlag, 2005: 208-219.
[13] Hertel D. Cross-correlation between GMW and dillon-dobbertinsequences[J]. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006, E89-A(9): 2264-2267.
[14] 佟鑫, 温巧燕. GMW序列和WG序列及WG序列间的互相关特性[J]. 通信学报, 2007, 28(7): 118-122. Tong Xin, Wen Qiaoyan. Cross-correlation properties between GMW and WG sequences and that of WG sequences[J]. Journal on Communications, 2007, 28(7): 118-122.
[15] Arasu K T, Ding C, Helleseth T, et al. Almost difference sets and their sequences with optimal autocorrelation[J]. IEEE Trans Inform Theory, 2001, 47(7): 2934-2943.

CrossCorrelation Properties of Perfect Binary Sequences

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	DU Jiao, WEN Qiao-yan, ZHANG Jie, PANG Shan-qi, LIAO Xin. Construction and Counting of Resilient 2-Rotation Symmetric Boolean Functions with 2p Variables [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2012, 35(5): 36-40.
[2]	. A Privacy-Preserving Dynamic Point-Point Distance Determination Protocol and Its Extension [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2012, 35(3): 47-51.
[3]	. Probability Distribution of XOR Difference between  Ones Complement Addition and XOR [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2011, 34(2): 35-38.
[4]	CHEN Shi-wei, JIN Chen-hui, LI Xi-bin. Analysis on the Consistent Degree of Addition Modulo 2ⁿwith XOR and Its Application [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2010, 33(3): 44-47.
[5]	MA Min-yao1, LUO Shou-shan1,2, WANG Li-cheng1 . Secure Two-party Computation Protocols for Mapping-equivalence Problem [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2008, 31(6): 5-8.
[6]	ZUO Hui-juan1,2, Tong Xin2 , WEN Qiao-yan2. Constructions of ZCZ Sequence Set from a Perfect Sequence [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2008, 31(4): 122-125.
[7]	SUN Ying1, QIN Su-juan1, WEN Qiao-yan1, ZHU Fu-chen2. 利用GHZ态实现可控的量子秘密共享 [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2008, 31(1): 9-13.
[8]	ZHANG Wei-guo1, DING Yong2, ZHANG Ning1， XIAO Guo-zhen1. A Characterization of Algebraic Immune Boolean Functions [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2007, 30(5): 55-57.
[9]	TONG Xin1, WEN Qiao-yan1, ZHU Fu-chen2. Quantum Secret Sharing Based on GHZ States Entanglement Swapping [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2007, 30(1): 44-48.
[10]	MO Jiao , WEN Qiao-yan. The Construction and Enumeration of Symmetric Balanced Boolean Functions with Even Number of Variables [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(6): 25-27.
[11]	WANG Biao1-3 , YANG Xiao-dong1 , HUANG Hai-ning3 . A Group Signature Scheme Based on the Weil Pairing [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(s2): 133-135.
[12]	MO Jiao , WEN Qiao-yan. The Construction and Enumeration of Symmetric Balanced Boolean Functions [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(5): 15-18.
[13]	ZHANG Wen-ying¹，WU Chuan-kun¹，LEI Hong². A New Cheating Immune Secret Sharing Function [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(4): 54-56.
[14]	CHANG Zu-ling^1，2，KE Pin-hui^1，2，MO Jiao¹, WEN Qiao-yan¹. On Properties and Constructions of Hyper-bent Functions [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(3): 36-39.
[15]	YANG Yu-guang¹WEN Qiao-yan¹ ZHU Fu-chen². Quantum Key Distribution and Secret Sharing via W states [J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2006, 29(3): 40-43.