中文摘要：

现在直角的数组在统计，计算机科学，编码理论和密码学起重要作用。平常的差别矩阵为许多混合直角的数组的构造是必要的。但是也有许多直角的数组，特别混合级或不均匀它不能被平常的差别矩阵获得。以便构造这些不均匀的直角的数组，特殊矩阵的一个类，所谓的概括差别矩阵，被张发现(1989， 1990,1993 ) 由射影的矩阵的直角的分解。在这篇文章，在直角的数组和概括差别矩阵之间的一种有趣的相等的关系被介绍。作为一个应用程序，跑尺寸 4p2 的直角的数组的一个家庭例如 L36 (6134210 ) ，被构造。

英文摘要：

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. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.