Abstract:
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.
Keywords:orthogonal arrays, Hamming distance distribution, nonnegative integer solution of a linear system.
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