Journal of Combinatorial Optimization

, Volume 35, Issue 4, pp 1061–1085 | Cite as

A feasibility approach for constructing combinatorial designs of circulant type

  • Francisco J. Aragón Artacho
  • Rubén Campoy
  • Ilias Kotsireas
  • Matthew K. Tam


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.


Strassler’s table Circulant weighing matrices Circulant combinatorial designs Douglas–Rachford algorithm 



We would like to thank an anonymous referee for their careful reading and suggestions, which helped us to improve the manuscript. We would also like to thank Yossi Strassler for sending us a scan of his original table. This research was enabled, in part, thanks to support provided by Compute Canada and their Graham petascale supercomputer.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Francisco J. Aragón Artacho
    • 1
  • Rubén Campoy
    • 1
  • Ilias Kotsireas
    • 2
  • Matthew K. Tam
    • 3
  1. 1.Department of MathematicsUniversity of AlicanteAlicanteSpain
  2. 2.CARGO LabWilfrid Laurier UniversityWaterlooCanada
  3. 3.Institut für Numerische und Angewandte MathematikUniversität GöttingenGöttingenGermany

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