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Keywords:

  • Hadamard matrices;
  • classification of combinatorial objects;
  • isomorph-free generation;
  • orderly algorithm

Abstract

Two Hadamard matrices are considered equivalent if one is obtained from the other by a sequence of operations involving row or column permutations or negations. We complete the classification of Hadamard matrices of order 32. It turns out that there are exactly 13,710,027 such matrices up to equivalence.