Balanced ternary and quaternary sequence pairs of odd period with three-level correlation

Lianfei Luo, Wenping Ma


Sequence pairs with good correlation have wide applications in communication systems. In this paper, ternary and quaternary sequence pairs of odd period with three-level correlation are constructed based on cyclotomy. In our constructions, sequences are both balanced and the maximum out-of-phase cross-correlation magnitude is shown to be √7 for ternary sequence pairs and to be √5 for quaternary sequence pairs, which are both better than the known sequence pairs of odd period with three-level correlation. 


balance; ternary sequence pair; quaternary sequence pair; three-level correlation; cyclotomy


Arasu, K.T., Ding, C., Helleseth, T., Kumar, P.V. & Martinsen, H. (2001). Almost difference sets and their sequences with optimal autocorrelation. IEEE Trans Inf Theory 47(7): 2934-2943.

Cai, Y. & Ding, C. (2009). Binary sequences with optimal autocorrelation. Theoret Comput Sci 410(24-25): 2316-2322.

Chung, J., No, J. & Chung, H. (2011). A construction of a new family of M-ary sequences with low correlation from Sidel’nikov sequences. IEEE Trans Inf Theory 57(4): 2301-2305.

Fan, P. & Darnell, M. (1996). Sequence Design for Communications Applications. Research Studies Press, London.

Golomb, S.W. & Gong, G. (2005). Signal Design for Good Correlation-For Wireless Communication, Cryptography and Radar. Cambrideg University Press, Cambridge.

Jin, H. & Xu, C. (2010). The study of methods for constructing a family of pseudorandom binary sequence pairs based on the cyclotomic class. Acta Electronica Sinica 38: 1608-1611.

Krone, S.M. & Sarwate, D.V. (1984). Quadriphase sequences for spread spectrum multiple access communication. IEEE Trans Inf Theory 30(3): 520-529.

Li, S., Luo, L. & Zhao, H. (2016). A class of almost $r$-phase sequences with ideal autocorrelation. Kuwait Journal of Science, 43(1): 1-14.

Luke, H.D., Schotten, H.D. & Hadinejad-Mahram H. (2000). Generalised Sidelnikov sequences with optimal autocorrelation properties. Electronics Letters 36(6): 525-527.

Peng, X., Xu, C. & Arasu, K.T. (2012). New families of binary sequence pairs with two-level and three-level correlation. IEEE Trans Inf Theory 58(11): 6968-6978.

Peng, X., Xu, C. & Li, G. (2012). Even period quaternary sequence pair with three-level autocorrelation. Systems Engineering & Electronics 34(10): 1999-2004.

Peng, X., Xu, C., Li, G., Liu, K. & Arasu, K.T. (2011). The constructions of almost binary sequence pairs and binary sequence pairs with three-level autocorrelation. IEICE Trans Fundament E94-A(9): 1886-1891.

Rohling, H. & Plagge, W. (1989). Mismatched filter design for periodical binary phased signals. IEEE Trans Aerosp Electron Syst 26: 890-897.

Storer, T. (1967). Cyclotomy and difference sets, Markham, Chicago.

Sze, T.W., Chanson, S., Ding, C., Helleseth, T. & Parker, M. (2003). Logarithm cartesian authentication codes. Information and Computation 184(1): 93-108.

Shen, X., Jia, Y. & Song, X. (2017). Constructions of binary sequence pairs of period 3p with optimal three-level correlation. IEEE Communications Letters 21(10): 2150-2153.

Tang, X. & Lindner, J. (2009). Almost quadriphase sequence with ideal autocorrelation property. IEEE Signal Processing Letters 16(1): 38-40.

Tang, X. & Gong, G. (2010). New constructions of binary sequences with optimal autocorrelation value/magnitude. IEEE Trans Inf Theory 56(3): 1278-1286.


  • There are currently no refbacks.

Copyright (c) 2019 Lianfei Luo, Wenping Ma

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.