| A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2 |
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| 引用本文： | 廖靖宇 张建军 张应山. A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2[J]. 数学季刊, 2007, 22(3): 426-435 |
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| 作者姓名： | 廖靖宇 张建军 张应山 |
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| 作者单位： | [1]Department of Mathematics, Xuchang College, Xuchang 461000, China [2]Department of Statistics, East China Normal University, Shanghai 200062, China |
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| 基金项目： | Supported by the National Science Foundations of China（10571045）; Supported by the National Science Foundations of Henan Province（0224370051; 0211063100） |
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| 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.
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| 关 键 词： | 试验次数 非对称正交表 构造方法 4p^2 广义养分矩阵 |
| 文章编号： | 1002-0462（2007）03-0426-10 |
| 收稿时间： | 2007-01-13 |
| 修稿时间： | 2007-01-13 |
A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2 |
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| Abstract: | 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(6134210), are constructed. |
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| Keywords: | mixed-level orthogonal arrays generalized difference matrices projective matrices permutable matrices |
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