Using a backtracking algorithm along with an essential change to the rows of representatives of known 13 710 027 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.

中文翻译：

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32阶偏Hadamard矩阵的分类和31阶关联方案

使用回溯算法以及对阶数为32的Hadamard矩阵的已知13 710 027等价类的代表行进行必要的更改，我们使穷举计算机搜索变得可行，并表明确实存在6662阶的不等价偏斜Hadamard矩阵如果两个偏斜Hadamard矩阵在一个有符号置换矩阵中相似，则视为SH等效。我们确定，直到SH等效为止，精确存在3227阶的7227斜哈达玛矩阵 。这部分解决了Kim和Solé提出的问题。因此，我们提供了31阶关联方案的分类。