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Keywords:

  • Hadamard matrices;
  • supplementary difference sets;
  • hashing

Abstract

We construct Hadamard matrices of orders inline image and inline image, and skew-Hadamard matrices of orders inline image and inline image. As far as we know, such matrices have not been constructed previously. The constructions use the Goethals–Seidel array, suitable supplementary difference sets on a cyclic group and a new efficient matching algorithm based on hashing techniques.