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A Novel Method for Constructing Almost Perfect Polyphase Sequences

  • Xiangyong Zeng
  • Lei Hu
  • Qingchong Liu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)

Abstract

This paper proposes a novel method of constructing almost perfect polyphase sequences based on the shift sequence associated with a primitive polynomial f(x) of degree 2J over finite field GF(p) (p odd prime, J=1,2,⋯) and a pair of almost perfect sequences completely orthogonal. Almost perfect polyphase sequences of length 2(p J +1) are constructed with phases as any positive even number. New families of almost perfect polyphase sequences in other lengths are also provided. In particular, several new families of almost perfect quadriphase sequences of lengths m(p J +1) are attained, where m=4 or 8, and p J –1≡0 (mod m).

Keywords

Periodic autocorrelation almost perfect sequence quadriphase sequence binary sequence 

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References

  1. 1.
    Brown, R.F., Goodwin, G.C.: New class of pseudorandom binary sequences. IEE Electron. Lett. 3, 198–199 (1967)CrossRefGoogle Scholar
  2. 2.
    Wolfmann, J.: Almost perfect autocorrelation sequence. IEEE Trans. Inform. Theor. 38, 1412–1418 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Langevin, P.: Almost perfect binary sequences. Appl. Algebra in Eng., Commun. Comput. 4, 95–102 (1993)CrossRefzbMATHGoogle Scholar
  4. 4.
    Pott, A., Bradley, S.P.: Existence and nonexistence of almost-perfect autocorrelation sequences. IEEE Trans. Inform. Theor. 41, 301–303 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Lüke, A.: Almost-perfect quadriphase sequences. IEEE Trans. Inform. Theor. 47, 2607–2608 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gong, G.: Theory and application of q-ary interleaved sequences. IEEE Trans. Inform. Theor. 41, 400–411 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Gong, G.: New designs for signal sets with low cross correlation, balance property, and large linear span, GF(p) case. IEEE Trans. Inform. Theor. 48, 2847–2867 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Games, R.A.: Crosscorrelation of M-sequences and GMW sequences with the same primitive polynomial. Discrete Applied Mathematics 12, 146–149 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chan, A.H., Games, R.A.: On the linear span of binary sequences obtained from q-ary m-sequences, q odd. IEEE Trans. Inform. Theor. 36, 548–552 (1990)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiangyong Zeng
    • 1
    • 3
  • Lei Hu
    • 2
  • Qingchong Liu
    • 3
  1. 1.The Faculty of Mathematics and Computer ScienceHubei UniversityWuhanChina
  2. 2.The State Key Laboratory of Information Security (Graduate School of Chinese Academy of Sciences)BeijingChina
  3. 3.Department of Electrical and System EngineeringOakland UniversityRochesterUSA

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