Journal of Combinatorial Optimization

, Volume 22, Issue 4, pp 873–881 | Cite as

A modified power spectral density test applied to weighing matrices with small weight

  • Ilias S. Kotsireas
  • Christos Koukouvinos
  • Panos M. Pardalos


The power spectral density test has been used for at least a decade in the search for many kinds of combinatorial matrices, such as weighing matrices for instance. In this paper we establish a modified power spectral density test that we apply to the search for weighing matrices of small weights constructed from two circulants. The main novelty of our approach is to define the Discrete Fourier Transform on the support of the first rows of the two circulants, thus exploiting the inherent sparsity of the problem. This new formalism turns out to be very efficient for small weights 9,18,36 and we find 10 new weighing matrices W(2⋅p,18) for prime p∈{37,47,53,59,61,67,73,79,83,97}. These matrices are given here for the first time. We also discuss briefly a connection with Combinatorial Optimization.


Weighing matrices Algorithm Sparsity Support 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Ilias S. Kotsireas
    • 1
  • Christos Koukouvinos
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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