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Paper   IPM / M / 15993
School of Mathematics
  Title:   Classification of skew-Hadamard matrices of order 32 and association schemes of order 31
  Author(s):  Behruz Tayfeh-Rezaie (Joint with A. Hanaki, H. Kharaghani, and A. Mohammadian)
  Status:   Published
  Journal: J. Combin. Des.
  Vol.:  28
  Year:  2020
  Pages:   421-427
  Supported by:  IPM
sing a backtracking algorithm along with an essential change to the rows of representatives of known 13710027 equivalence classes of Hadamard matrices of order 32, we make an exhaustive computer search feasible and show that there are exactly 6662 inequivalent skew-Hadamard matrices of order 32. Two skew-Hadamard matrices are considered SH-equivalent if they are similar by a signed permutation matrix. We determine that there are precisely 7227 skew-Hadamard matrices of order 32 up to SH-equivalence. This partly settles a problem posed by Kim and Solé. As a consequence, we provide the classification of association schemes of order 31.

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