Nowadays orthogonal arrays play important roles in statistics,computer science,coding theory and cryptography.The usual difference matrices are essential for the construction of many mixed orthogonal arrays,however there are also orthogonal arrays which can not be obtained by the usual difference matrices.In order to construct these mixed orthogonal arrays,a class of special matrices socalled generalized difference matrices were discovered by Zhang (1989,1990,1993)from the orthogonal decompositions of projection matrices.An interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is introduced.As an application,a lot of new orthogonal arrays of run size 84 were constructed.%当今,正交表在统计、计算机、编码和译码等领域起着重要的作用.普通的差矩阵在构作正交表中是基本的工具.但也有许多正交表不能用普通的差矩阵构作.为了构作这些特殊的正交表,张(1989,1990,1993)利用投影矩阵的正交分解,发现了一类特殊的矩阵,称为广义差矩阵.本文中,广义差矩阵与正交表的一个有趣的关系被提出.作为应用,一系列84次试验的非对称正交表被构造.
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