Annals of Combinatorics

, 13:305 | Cite as

Weighing Matrices and String Sorting

  • Ilias S. Kotsireas
  • Christos Koukouvinos
  • Jennifer Seberry


In this paper we establish a fundamental link between the search for weighing matrices constructed from two circulants and the operation of sorting strings, an operation that has been studied extensively in computer science. In particular, we demonstrate that the search for weighing matrices constructed from two circulants using the power spectral density criterion and exploiting structural patterns for the locations of the zeros in candidate solutions, can be viewed as a string sorting problem together with a linear time algorithm to locate common strings in two sorted arrays. This allows us to bring into bear efficient algorithms from the string sorting literature. We also state and prove some new enhancements to the power spectral density criterion, that allow us to treat successfully the rounding error effect and speed up the algorithm. Finally, we use these ideas to find new weighing matrices of order 2n and weights 2n – 13, 2n – 17 constructed from two circulants.

AMS Subject Classification

05B20 62K05 


weighing matrices algorithm pattern locations of zeros power spectral density rounding error 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Ilias S. Kotsireas
    • 1
  • Christos Koukouvinos
    • 2
  • Jennifer Seberry
    • 3
  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece
  3. 3.Centre for Computer Security Research, School of Information Technology and Computer ScienceUniversity of WollongongWollongongAustralia

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