Odd Perfect Sequences and Sets of Spreading Sequences with Zero or Low Odd Periodic Correlation Zone

  • Yang Yang
  • Guang Gong
  • Xiaohu Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)


In this paper, we apply shift sequences defined by difference balanced function with d-form property to construct (almost) perfect or odd perfect sequences, which is a generalization of the construction given by Krengel in 2004. We then propose new signal sets with flexible parameters and zero odd periodic correlation zone or low odd periodic correlation zone property, by interleaving an odd perfect sequence or a sequence with low odd periodic correlation. Furthermore, we show that the parameters of some constructed signal sets are optimal with respect to the odd periodic correlation bound.


Periodic correlation odd periodic correlation low (odd periodic) correlation zone zero (odd periodic) correlation zone difference balanced functions 


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  1. 1.
    Antweiler, M.: Cross-Correlation of p-ary GMW Sequences. IEEE Trans. Inform. Theory 40(4), 1253–1261 (1994)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Chung, J.-H., Yang, K.: New design of quaternary low-correlation zone sequence sets and quaternary hadamard matrices. IEEE Trans. Inform. Theory 54(8), 3733–3737 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fan, P.Z., Suehiro, N., Kuroyanagi, N., Deng, X.M.: Class of binary sequences with zero correlation zone. Electronics Letters 35(10), 777–779 (1999)CrossRefGoogle Scholar
  4. 4.
    Golomb, S.W., Gong, G.: Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005)MATHCrossRefGoogle Scholar
  5. 5.
    Gong, G.: Theory and applications of q-ary interleaved sequences. IEEE Trans. Inform. Theory 41(2), 400–411 (1995)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Gong, G., Golomb, S.W., Song, H.-Y.: A note on low-correlation zone signal sets. IEEE Trans. Inform. Theory 53(7), 2575–2581 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gaudenzi, R.D., Elia, C., Viola, R.: Bandlimited quasisynchronous CDMA: A novel satellite access technique for mobile and personal communication systems. IEEE J. Sel. Areas Commun. 10(2), 328–343 (1992)CrossRefGoogle Scholar
  8. 8.
    Hayashi, T.: A class of ternary sequence sets with a zero-correlation zone for periodic, aperiodic, and odd correlation functions. IEICE Trans. Fundamentals E86-A(7), 1850–1857 (2003)Google Scholar
  9. 9.
    Hayashi, T.: Zero correlation zone sequence set constructed from a perfect sequence. IEICE Trans. Fundamentals E90-A(5), 1–5 (2007)Google Scholar
  10. 10.
    Hayashi, T.: Ternary sequence set having periodic and aperiodic zero-correlation zone. IEICE Trans. Fundamentals E89-A(6), 1825–1831 (2006)CrossRefGoogle Scholar
  11. 11.
    Helleseth, T., Gong, G.: New binary sequences with ideal-level autocorrelation function. IEEE Trans. Inform. Theory 154(18), 2868–2872 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hu, H.G., Gong, G.: New sets of zero or low correlation correlation zone via interleaving techniques. IEEE Trans. Inform. Theory 56(4), 1702–1713 (2010)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Jang, J.-W., No, J.-S., Chung, H., Tang, X.H.: New sets of optimal p-ary low-correlation zone sequences. IEEE Trans. Inform. Theory 53(2), 815–821 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    No, J.-S.: New cyclic diffrence sets with Singer parameters constructed from d-homogeneous function. Des., Codes, Cryptogr. 33, 199–213 (2004)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Klapper, A.: d-form sequence: Families of sequences with low correlaltion values and large linear spans. IEEE Trans. Inform. Theory 51(4), 1469–1477 (1995)Google Scholar
  16. 16.
    Krengel, E.I.: Almost-Perfect and Odd-Perfect Ternary Sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 197–207. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Krengel, E.I.: Some Constructions of Almost-Perfect, Odd-Perfect and Perfect Polyphase and Almost-Polyphase Sequences. In: Carlet, C., Pott, A. (eds.) SETA 2010. LNCS, vol. 6338, pp. 387–398. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Lüke, H.D., Schotten, H.D.: Odd-perfect almost binary correlation sequences. IEEE Trans. Aerosp. Electron. Syst. 31, 495–498 (1995)CrossRefGoogle Scholar
  19. 19.
    Lüke, H.D.: Sets of ternary sequences with odd periodic zero correlation zones. Frequenz. 58, 214–216 (2004)CrossRefGoogle Scholar
  20. 20.
    Lüke, H.D., Schotten, H.D.: Binary and quadriphase sequence with optimal autocorrelation: A survey. IEEE Trans. Inform. Theory 49(12), 3271–3282 (2003)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Parker, M.G.: Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation. In: Boztaş, S., Sphparlinski, I.E. (eds.) AAECC 2001. LNCS, vol. 2227, pp. 200–209. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Popovic, B.M., Mauritz, O.: Generalized Chirp-like sequences with zero correlation zone. IEEE Trans. Inform. Theory 56(6), 2957–2960 (2010)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Tang, X.H., Fan, P.Z., Matsufuji, S.: Lower bounds on the maximum correlation of sequence set with low or zero correlation zone. Electron. Lett. 36(6), 551–552 (2000)CrossRefGoogle Scholar
  24. 24.
    Tang, X.H., Fan, P.Z.: Bounds on aperiodic and odd correlation with low or zero correlation zone. Electron. Lett. 37(19), 1201–1203 (2001)CrossRefGoogle Scholar
  25. 25.
    Tang, X.H., Fan, P.Z.: A class of pseudonise sequences over GF(p) with low correlation zone. IEEE Trans. Infrom. Theory 47(4), 1644–1649 (2001)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Tang, X.H., Mow, W.H.: A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences. IEEE Trans. Inform. Theory 54(12), 5729–5735 (2008)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Suehiro, N.: Approximately synchronized CDMA system without cochannel using pseudo-periodic sequences. In: Proceedings of 1993 International Symposium on Personal Communications, Nanjing, China, pp. 179–184 (October 1994)Google Scholar
  28. 28.
    Tang, X.H.: A note on d-form function with differencebalanced property (preprint)Google Scholar
  29. 29.
    Zhou, Z.C., Tang, X.H., Gong, G.: A new class of sequences with zero or low correlation zone based on interleaving technique. IEEE Trans. Inform. Theory 54(9), 4267–4273 (2008)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yang Yang
    • 1
    • 2
  • Guang Gong
    • 2
  • Xiaohu Tang
    • 1
  1. 1.Institute of Mobile CommunicationsSouthwest Jiaotong UniversityChengduPRC
  2. 2.Department of Electrical and Computer EngineeringUniversity of WaterlooWaterlooCanada

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