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Inner Product Vectors for Skew-Hadamard Matrices

  • Ilias S. Kotsireas
  • Jennifer Seberry
  • Yustina S. Suharini
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 133)

Abstract

Algorithms to find new orders of skew-Hadamard matrices by complete searches are not efficient and require extensive CPU time. We consider a method relying on pre-calculation of inner product vectors aiming to reduce the search space. We apply our method to the algorithm of Seberry–Williamson to construct skew-Hadamard matrices. We find all possible solutions for ≤ 29. We use these results to improve analysis in order to reduce the search space.

Keywords

Hadamard matrices Seberry-Williamson array Skew-Hadamard matrices Good matrices Supplementary difference sets 05B20 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ilias S. Kotsireas
    • 1
  • Jennifer Seberry
    • 2
  • Yustina S. Suharini
    • 3
  1. 1.Department of Physics & Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Centre for Computer and Information Security Research, SCSSEUniversity of WollongongWollongongAustralia
  3. 3.Department of Informatics EngineeringInstitute of Technology IndonesiaBantenIndonesia

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