Two new classes of binary sequence pairs with three-level cross-correlation
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Abstract
A pair of binary sequences is generalized from the concept of a two-level autocorrelation function of single binary sequence. In this paper, we describe two classes of binary sequence pairs of period $N=2q$, where $q=4f+1$ is an odd prime and $f$ is an even integer. Those classes of binary sequence pairs are based on cyclic almost difference set pairs. They have optimal three-level cross-correlation, and either balanced or almost balanced.-
Keywords:
- Binary sequence pair,
- almost difference set pair,
- three-level cross-correlation,
- optimal correlation value,
- cyclotomy.
Mathematics Subject Classification: Primary: 05B10; Secondary: 94A55.Citation: -
References
[1] L. D. Baumert, Cyclic Difference Sets, Springer-Verlag, 1971.
[2] T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, North-Holland/Elsevier, Amsterdam, 1998.
[3] L. E. Dickson, Cyclotomy, higher congruences, and Waring's problem, Amer. J. Math., 57 (1935), 391-424.doi: 10.2307/2371217.
[4] C. Ding, T. Helleseth and K. Y. Lam, Several classes of binary sequences with three-level autocorrelation, IEEE Trans. Inf. Theory, 45 (1999), 2606-2612.doi: 10.1109/18.796414.
[5] C. Ding, T. Helleseth and H. Martinsen, New families of binary sequences with optimal three-level autocorrelation, IEEE Trans. Inf. Theory, 47 (2001), 428-433.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), 1608-1611.
[8] S. Y. Jin and H. Y. Song, Note on a pair of binary sequences with ideal two-level crosscorrelation, in Proc. ISIT2009, Seoul, 2009, 2603-2607.
[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, 259-295.
[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), 10-14.
[11] K. Liu and C. Q. Xu, On binary sequence pairs with two-level periodic cross-correlation function, IEICE Trans. Funda., E93-A (2010), 2278-2285.
[12] F. Mao, T. Jiang, C. L. Zhao and Z. Zhou, Study of pseudorandom binary sequence pairs (in Chinese), J. Commun., 26 (2005), 94-98.
[13] X. P. Peng, C. Q. Xu and K. T. Arasu, New families of binary sequence pairs with two-level and three-level correlation, IEEE Trans. Inf. Theory, 58 (2012), 2968-2978.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), 93-108.doi: 10.1016/S0890-5401(03)00053-1.
[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), 692-695.
[17] C. Q. Xu, Difference set pairs and approach for the study of perfect binary array pairs (in Chinese), Acta Electr. Sin., 29 (2001), 87-89.
[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), 34-37.
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