Orthogonal arrays play an important role in statistics and experimental design. Like other combinatorial constructions, the most important and studied problems are questions about their existence and classification. An essential step to solving such problems is determination of Hamming distance distributions of an orthogonal array with given parameters. In this paper we propose an algorithm for computing possible distance distributions of an orthogonal array with arbitrary parameters with respect to any vector of the space. The possible distance distributions are all nonnegative integer solutions of special linear systems with integer coefficients. The proposed algorithm reduces the problem to checking signs of only t + 1 coordinates of vectors of a subset of integer solutions of the system.

中文翻译：

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正交阵列的距离分布

正交阵列在统计和实验设计中起着重要作用。像其他组合结构一样，最重要且已研究的问题是有关其存在和分类的问题。解决此类问题的必要步骤是确定具有给定参数的正交阵列的汉明距离分布。在本文中，我们提出了一种算法，用于计算相对于空间的任何矢量具有任意参数的正交阵列的可能距离分布。可能的距离分布是具有整数系数的特殊线性系统的所有非负整数解。所提出的算法将问题简化为仅检查系统整数解的子集的矢量的t + 1坐标的符号。