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On the correlation of sequences

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Algebraic Coding (Algebraic Coding 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 573))

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Abstract

In code division multiple access applications it is necessary to find sequences with small maximum nontrivial correlation C max. In this paper we show that the moduli of certain character sums can be calculated in a very easy way by using a modification of a method of Sidelnikov. These results yield a very simple way to calculate C max for nonbinary sequences found by Kumar and Moreno and for those found by Liu and Komo.

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References

  1. P. Vijay Kumar and Chao-Ming Liu: On lower bounds to the maximum correlation of complex roots of-unity sequences.-IEEE Transactions on Information Theory 36 (1990), 633–640.

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  2. P. Vijay Kumar and Oscar Moreno: Polyphase sequences with periodic correlation properties better than binary sequences. — IEEE Transactions on Information Theory (submitted).

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  3. Shyh-Chang Liu and John J. Komo: Nonbinary Kasami sequences over GF(p). — IEEE Transactions on Information Theory (submitted).

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  4. V.M. Sidelnikov: On mutual correlation of sequences.-Problemy Kibernetiki 24 (1971), 15–42 (in Russian).

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  5. P. Solé: A quaternary cyclic code and a family of quadriphase sequences with low correlation properties. — Coding Theory and Applications (Eds. G. Cohen and J. Wolfmann), Lecture Notes in Computer Science 388, Springer-Verlag (1989), 193–201.

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  6. Hannu Tarnanen: On character sums and codes.-Discrete Mathematics 57 (1985), 285–295.

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  7. L.R. Welch: Lower bounds on the maximum correlation of signals.-IEEE Transactions on Information Theory 20 (1974), 397–399.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, SF-20500, Turku, Finland

    A. Tietäväinen

Authors
  1. A. Tietäväinen
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Gérard Cohen Antoine Lobstein Gilles Zémor Simon Litsyn

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© 1992 Springer-Verlag Berlin Heidelberg

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Tietäväinen, A. (1992). On the correlation of sequences. In: Cohen, G., Lobstein, A., Zémor, G., Litsyn, S. (eds) Algebraic Coding. Algebraic Coding 1991. Lecture Notes in Computer Science, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034334

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  • DOI: https://doi.org/10.1007/BFb0034334

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55130-0

  • Online ISBN: 978-3-540-46739-7

  • eBook Packages: Springer Book Archive

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