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Evolutionary Search for Binary Strings with Low Aperiodic Auto-correlations

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Artificial Evolution (EA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2936))

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Abstract

In this paper we apply evolutionary methods to find finite binary ±1-sequences with low out-of-phase aperiodic auto-correlations. These sequences have important applications in communication or statistical mechanics, but their construction is a difficult computational problem. The Golay Factor of Merit is studied from a probabilistic point of view, in order to explain the poor efficiency of evolutionary algorithms. Various genetic algorithms are then proposed and tested.

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References

  1. Beenker, G.F.M., Claasen, T.A.C.M., Hermens, P.W.C.: Binary sequences with maximally flat amplitude spectrum. Philips J. Res. 40, 289–304 (1985)

    MATH  Google Scholar 

  2. Bernasconi, J.: Low autocorrelation binary sequences: statistical mechanics and configuration space analysis. J. Physique 48, 559 (1987)

    Article  Google Scholar 

  3. Golay, M.J.E.: The merit factor of long low autocorrelation binary sequences. IEEE Trans. Inf. theory IT-23, 43–51 (1982)

    Google Scholar 

  4. Golay, M.J.E.: The merit factor of Legendre sequences. IEEE Trans. Inf. theory IT-29, 934–936 (1983)

    Article  Google Scholar 

  5. de Groot, C., Würtz, D., Hoffmann, K.H.: Low Autocorrelation Binary Sequences: Exact Enumeration and Optimization by Evolutionary Strategies. Optimization 23, 369–384 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. Høholdt, T.: The Merit Factor of Binary sequences. In: pott, A., et al. (eds.) Difference Sets, Sequences and their Correlation Properties. Series C: mathematical and Physical Sciences, vol. 542, pp. 227–237. Kluwer Acad. Publish, Dordrecht (1999)

    Google Scholar 

  7. Jensen, J.M., Elbrønd Jensen, H., Høholdt, T.: The Merit Factor of Binary Sequences Related to Difference Sets. IEEE Trans. Inform. Theory 37-3, 617–626 (1991)

    Article  Google Scholar 

  8. Knuth, D.E.: The Art of Computer Programming, 2nd edn. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  9. Mertens, S.: Exhaustive search for low-autocorrelation binary sequences. J. Phys. A: Math. Gen. 29, 473–481 (1996)

    Article  MathSciNet  Google Scholar 

  10. Parker, M.G.: Even Length Binary Sequence Families with Low Negaperiodic Autocorrelation. In: Bozta, S., Sphparlinski, I. (eds.) AAECC 2001. LNCS, vol. 2227, pp. 200–210. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Prestwich, S.: A Hybrid Local Search Algorithm for Low-Autocorrelation Binary Sequences, Tech. Report TR-00-01, Dept. Comp. Sci., National Univ. Ireland at Cork, pp. 14

    Google Scholar 

  12. Schroeder, M.R.: Number Theory in Science and Communication. Springer, Berlin (1984)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d’Informatique, École Polytechnique de l’Université de Tours, 64, Av. Jean Portalis, 37200, Tours, France

    Sebastien Aupetit & Mohamed Slimane

  2. Laboratoire ATP, UMR-CNRS no. 6632, Université de Provence, Centre de Mathématiques Informatique et Mécanique, 39, rue F. Joliot-Curie, 13453, Marseille cedex 13, France

    Pierre Liardet

Authors
  1. Sebastien Aupetit
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  2. Pierre Liardet
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  3. Mohamed Slimane
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Editor information

Editors and Affiliations

  1. UMR-CNRS 6632, Université de Provence, 39 rue F. Joliot-Curie, 13453, Marseille cedex 13, France

    Pierre Liardet

  2. Université Louis Pasteur, LSIIT, FDBT, Pôle API, F-67400, Illkirch, France

    Pierre Collet

  3. Laboratoire d’Informatique du Littoral, Maison de la Recherche Blaise Pascal, 50 rue Ferdinand Buisson, BP 719, 62228, Calais Cedex, France

    Cyril Fonlupt

  4. INRIA Saclay - Ile-de-France, Parc Orsay Université, 4, rue Jacques Monod, 91893, Orsay Cedex, France

    Evelyne Lutton

  5. TAO, INRIA Saclay & LRI (UMR CNRS 8623), Bât 490, Université Paris-Sud, 91405, Orsay Cedex, France

    Marc Schoenauer

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© 2004 Springer-Verlag Berlin Heidelberg

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Aupetit, S., Liardet, P., Slimane, M. (2004). Evolutionary Search for Binary Strings with Low Aperiodic Auto-correlations. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2003. Lecture Notes in Computer Science, vol 2936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24621-3_4

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  • DOI: https://doi.org/10.1007/978-3-540-24621-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21523-3

  • Online ISBN: 978-3-540-24621-3

  • eBook Packages: Springer Book Archive

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