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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. 
[2] 
T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, NorthHolland/Elsevier, Amsterdam, 1998. 
[3] 
L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math., 57 (1935), 391424. doi: 10.2307/2371217. 
[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. 
[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. 
[6] 
C. Ding, D. Pei and A. Salomaa, Chinese Remainder Theorem: Applications in Computing, Cryptography, World Scientific, Singapore, 1996. doi: 10.1142/9789812779380. 
[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. 
[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. 
[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. 
[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. 
[11] 
K. Liu and C. Q. Xu, On binary sequence pairs with twolevel periodic crosscorrelation function, IEICE Trans. Funda., E93A (2010), 22782285. 
[12] 
F. Mao, T. Jiang, C. L. Zhao and Z. Zhou, Study of pseudorandom binary sequence pairs (in Chinese), J. Commun., 26 (2005), 9498. 
[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. 
[14] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. 
[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. 
[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. 
[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. 
[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. 
show all references
References:
[1] 
L. D. Baumert, Cyclic Difference Sets, SpringerVerlag, 1971. 
[2] 
T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, NorthHolland/Elsevier, Amsterdam, 1998. 
[3] 
L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math., 57 (1935), 391424. doi: 10.2307/2371217. 
[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. 
[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. 
[6] 
C. Ding, D. Pei and A. Salomaa, Chinese Remainder Theorem: Applications in Computing, Cryptography, World Scientific, Singapore, 1996. doi: 10.1142/9789812779380. 
[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. 
[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. 
[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. 
[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. 
[11] 
K. Liu and C. Q. Xu, On binary sequence pairs with twolevel periodic crosscorrelation function, IEICE Trans. Funda., E93A (2010), 22782285. 
[12] 
F. Mao, T. Jiang, C. L. Zhao and Z. Zhou, Study of pseudorandom binary sequence pairs (in Chinese), J. Commun., 26 (2005), 9498. 
[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. 
[14] 
T. Storer, Cyclotomy and Difference Sets, Markham, Chicago, 1967. 
[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. 
[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. 
[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. 
[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. 
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