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A feasibility approach for constructing combinatorial designs of circulant type

Author

Listed:
  • Francisco J. Aragón Artacho

    (University of Alicante)

  • Rubén Campoy

    (University of Alicante)

  • Ilias Kotsireas

    (Wilfrid Laurier University)

  • Matthew K. Tam

    (Universität Göttingen)

Abstract

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.

Suggested Citation

  • Francisco J. Aragón Artacho & Rubén Campoy & Ilias Kotsireas & Matthew K. Tam, 2018. "A feasibility approach for constructing combinatorial designs of circulant type," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1061-1085, May.
    • Handle: RePEc:spr:jcomop:v:35:y:2018:i:4:d:10.1007_s10878-018-0250-5
    DOI: 10.1007/s10878-018-0250-5
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    References listed on IDEAS

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    1. Francisco J. Aragón Artacho & Jonathan M. Borwein & Matthew K. Tam, 2016. "Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem," Journal of Global Optimization, Springer, vol. 65(2), pages 309-327, June.
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