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Derived and residual subspace designs
Two new classes of binary sequence pairs with threelevel crosscorrelation
1.  School of Sciences, Nantong University, Nantong, Jiangsu 226007, China, China 
2.  Department of Mathematics, Guangxi Normal University, Guilin, Guangxi 541004, China 
References:
[1] 
L. D. Baumert, Cyclic Difference Sets, SpringerVerlag, 1971. Google Scholar 
[2] 
T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, NorthHolland/Elsevier, Amsterdam, 1998. Google Scholar 
[3] 
L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math., 57 (1935), 391424. doi: 10.2307/2371217. Google Scholar 
[4] 
C. Ding, T. Helleseth and K. Y. Lam, Several classes of binary sequences with threelevel autocorrelation, IEEE Trans. Inf. Theory, 45 (1999), 26062612. doi: 10.1109/18.796414. Google Scholar 
[5] 
C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal threelevel autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 428433. doi: 10.1109/18.904555. Google Scholar 
[6] 
C. Ding, D. Pei and A. Salomaa, Chinese Remainder Theorem: Applications in Computing, Cryptography, World Scientific, Singapore, 1996. doi: 10.1142/9789812779380. Google Scholar 
[7] 
H. L. Jin and C. Q. Xu, The study of methods for constructing a family of pseudorandom binary sequence pairs based on the cyclotomic class (in Chinese), Acta Electr. Sin., 38 (2010), 16081611. Google Scholar 
[8] 
S. Y. Jin and H. Y. Song, Note on a pair of binary sequences with ideal twolevel crosscorrelation, in Proc. ISIT2009, Seoul, 2009, 26032607. Google Scholar 
[9] 
D. Jungnickel and A. Pott, Difference sets: an introduction, in Difference Sets, Sequences and Their Correlation Properties (eds. A. Pott, P.V. Kumar, T. Helleseth and D. Jungnickel), Kluwer Academic Publishers, 1999, 259295. Google Scholar 
[10] 
J. Z. Li and P. H. Ke, Study on the almost difference set pairs and almost perfect autocorrelation binary sequence pairs (in Chinese), J. Wuyi University, 27 (2008), 1014. Google Scholar 
[11] 
K. Liu and C. Q. Xu, On binary sequence pairs with twolevel periodic crosscorrelation function, IEICE Trans. Funda., E93A (2010), 22782285. Google Scholar 
[12] 
F. Mao, T. Jiang, C. L. Zhao and Z. Zhou, Study of pseudorandom binary sequence pairs (in Chinese), J. Commun., 26 (2005), 9498. Google Scholar 
[13] 
X. P. Peng, C. Q. Xu and K. T. Arasu, New families of binary sequence pairs with twolevel and threelevel correlation, IEEE Trans. Inf. Theory, 58 (2012), 29682978. doi: 10.1109/TIT.2012.2210025. Google Scholar 
[14] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. Google Scholar 
[15] 
T. W. Sze, S. Chanson, C. Ding, T. Helleseth and M. G.Parker, Logarithm authentication codes, Infor. Comput., 148 (2003), 93108. doi: 10.1016/S08905401(03)000531. Google Scholar 
[16] 
Y. Z. Wang and C. Q. Xu, Divisible difference set pairs and approach for the study of almost binary sequence pair (in Chinese), Acta Electr. Sin., 37 (2009), 692695. Google Scholar 
[17] 
C. Q. Xu, Difference set pairs and approach for the study of perfect binary array pairs (in Chinese), Acta Electr. Sin., 29 (2001), 8789. Google Scholar 
[18] 
X. Q. Zhao, W. C. He, Z. W. Wang and S. L. Jia, The theory of the perfect binary array pairs (in Chinese), Acta Electr. Sin., 27 (1999), 3437. Google Scholar 
show all references
References:
[1] 
L. D. Baumert, Cyclic Difference Sets, SpringerVerlag, 1971. Google Scholar 
[2] 
T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, NorthHolland/Elsevier, Amsterdam, 1998. Google Scholar 
[3] 
L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math., 57 (1935), 391424. doi: 10.2307/2371217. Google Scholar 
[4] 
C. Ding, T. Helleseth and K. Y. Lam, Several classes of binary sequences with threelevel autocorrelation, IEEE Trans. Inf. Theory, 45 (1999), 26062612. doi: 10.1109/18.796414. Google Scholar 
[5] 
C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal threelevel autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 428433. doi: 10.1109/18.904555. Google Scholar 
[6] 
C. Ding, D. Pei and A. Salomaa, Chinese Remainder Theorem: Applications in Computing, Cryptography, World Scientific, Singapore, 1996. doi: 10.1142/9789812779380. Google Scholar 
[7] 
H. L. Jin and C. Q. Xu, The study of methods for constructing a family of pseudorandom binary sequence pairs based on the cyclotomic class (in Chinese), Acta Electr. Sin., 38 (2010), 16081611. Google Scholar 
[8] 
S. Y. Jin and H. Y. Song, Note on a pair of binary sequences with ideal twolevel crosscorrelation, in Proc. ISIT2009, Seoul, 2009, 26032607. Google Scholar 
[9] 
D. Jungnickel and A. Pott, Difference sets: an introduction, in Difference Sets, Sequences and Their Correlation Properties (eds. A. Pott, P.V. Kumar, T. Helleseth and D. Jungnickel), Kluwer Academic Publishers, 1999, 259295. Google Scholar 
[10] 
J. Z. Li and P. H. Ke, Study on the almost difference set pairs and almost perfect autocorrelation binary sequence pairs (in Chinese), J. Wuyi University, 27 (2008), 1014. Google Scholar 
[11] 
K. Liu and C. Q. Xu, On binary sequence pairs with twolevel periodic crosscorrelation function, IEICE Trans. Funda., E93A (2010), 22782285. Google Scholar 
[12] 
F. Mao, T. Jiang, C. L. Zhao and Z. Zhou, Study of pseudorandom binary sequence pairs (in Chinese), J. Commun., 26 (2005), 9498. Google Scholar 
[13] 
X. P. Peng, C. Q. Xu and K. T. Arasu, New families of binary sequence pairs with twolevel and threelevel correlation, IEEE Trans. Inf. Theory, 58 (2012), 29682978. doi: 10.1109/TIT.2012.2210025. Google Scholar 
[14] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. Google Scholar 
[15] 
T. W. Sze, S. Chanson, C. Ding, T. Helleseth and M. G.Parker, Logarithm authentication codes, Infor. Comput., 148 (2003), 93108. doi: 10.1016/S08905401(03)000531. Google Scholar 
[16] 
Y. Z. Wang and C. Q. Xu, Divisible difference set pairs and approach for the study of almost binary sequence pair (in Chinese), Acta Electr. Sin., 37 (2009), 692695. Google Scholar 
[17] 
C. Q. Xu, Difference set pairs and approach for the study of perfect binary array pairs (in Chinese), Acta Electr. Sin., 29 (2001), 8789. Google Scholar 
[18] 
X. Q. Zhao, W. C. He, Z. W. Wang and S. L. Jia, The theory of the perfect binary array pairs (in Chinese), Acta Electr. Sin., 27 (1999), 3437. Google Scholar 
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