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Autocorrelation via Runs

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Artificial Intelligence and Symbolic Computation (AISC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11110))

Abstract

A problem of interest in the realm of autocorrelation of (binary) finite sequences is to find sequences of length n with given (pre-defined) autocorrelation profiles. This amounts to solving a system of \(\lfloor n/2 \rfloor \) quadratic equations over the boolean cube \(\{-1,+1\}^n\). We establish and discuss a computational approach to this autocorrelation problems, using the concept of runs. An algorithm is given to solve this problem and its application is illustrated with non-trivial examples.

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Notes

  1. 1.

    The experiments are performed in Maple 2017 on a Windows PC with an Intel(R) Core(TM) i7-6700U CPU @3.40 GHz and 8 GB RAM. The program terminates with success after 7750 s and 14156 s, respectively.

References

  1. Brent, R.P., Orrick, W., Osborn, J.H., Zimmermann, P.: Maximal determinants and saturated D-optimal design of orders \(19\) and \(37\). arXiv: 1112.4160v1 (2015)

  2. Brent, R.P., Osborn, J.H.: General lower bounds on maximal determinants of binary matrices. Electron. J. Comb. 20(2), 12 (2013). Paper 15

    MathSciNet  MATH  Google Scholar 

  3. Brent, R.P., Osborn, J.H.: On minors of maximal determinant matrices. J. Integer Seq. 16(4), 30 (2013). Article 13.4.2

    MathSciNet  MATH  Google Scholar 

  4. Craigen, R., Kharaghani, H.: Hadamard matrices and Hadamard designs. In: Colbourn, C.J., Dinitz, J.H. (eds.) Handbook of Combinatorial Designs. Discrete Mathematics and Its Applications, 2nd edn, pp. 273–280. Chapman & Hall/CRC, Boca Raton (2007)

    Google Scholar 

  5. Dzokovic, D.Z., Kotsireas, I.S.: Compression of periodic complementary sequences and applications. Des. Codes Cryptogr. 74(2), 365–377 (2015)

    Article  MathSciNet  Google Scholar 

  6. Ehlich, H.: Determinantenabsschätzungen für binäre matrizen. Mathematische Z. 83, 517–531 (1964)

    Article  MathSciNet  Google Scholar 

  7. Hadamard, J.: Résolution dùne question relative aux déterminants. Bull. des Sci. Mathématiques 17, 240–246 (1893)

    MATH  Google Scholar 

  8. Kotsireas, I.S.: Algorithms and metaheuristics for combinatorial matrices. In: Pardalos, P., Du, D.Z., Graham, R. (eds.) Handbook of Combinatorial Optimization. Springer, New York (2013). https://doi.org/10.1007/978-1-4419-7997-1_13

    Chapter  Google Scholar 

  9. Orrick, W.P.: On the enumeration of some D-optimal designs. J. Stat. Plan. Inference 138(1), 286–293 (2008)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was made possible by the facilities of the SMS International at GXUN, Nanning, P.R. China. ISK’s work is supported by NSERC grants. JY’s work is supported by the Special Fund for Guangxi Bagui Scholars (WBS 2014-01) and the Startup Foundation for Advanced Talents in Guangxi University for Nationalities (2015MDQD018). ISK would like to thank JY for providing excellent working conditions at the SMS International and warm hospitality in Nanning.

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Authors and Affiliations

  1. Wilfrid Laurier University, Waterloo, ON, N2L 3C5, Canada

    Ilias S. Kotsireas

  2. SMS-HCIC, Guangxi University for Nationalities, Nanning, 530006, China

    Jing Yang

Authors
  1. Ilias S. Kotsireas
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  2. Jing Yang
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Correspondence to Jing Yang .

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Editors and Affiliations

  1. University of Edinburgh, Edinburgh, United Kingdom

    Jacques Fleuriot

  2. Beihang University, Beijing, China

    Dongming Wang

  3. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Jacques Calmet

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Kotsireas, I.S., Yang, J. (2018). Autocorrelation via Runs. In: Fleuriot, J., Wang, D., Calmet, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2018. Lecture Notes in Computer Science(), vol 11110. Springer, Cham. https://doi.org/10.1007/978-3-319-99957-9_13

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  • DOI: https://doi.org/10.1007/978-3-319-99957-9_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99956-2

  • Online ISBN: 978-3-319-99957-9

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