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 skewHadamard matrices of order 32. Two skewHadamard matrices are considered SHequivalent if they are similar by a signed permutation matrix. We determine that there are precisely 7227 skewHadamard matrices of order 32 up to SHequivalence. 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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