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Orthogonal arrays obtained by generalized difference matrices with g levels 被引量:11

Orthogonal arrays obtained by generalized difference matrices with g levels
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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 for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed. Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.
出处 《Science China Mathematics》 SCIE 2011年第1期133-143,共11页 中国科学:数学(英文版)
基金 supported by Visiting Scholar Foundation of Key Lab in University and by National Natural Science Foundation of China (Grant No. 10571045) Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No. 44k55050)
关键词 mixed-level orthogonal arrays generalized difference matrices projection matrices permutation matrices 正交阵列 差分矩阵 广义 计算机科学 编码理论 差别矩阵 正交分解 投影矩阵
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参考文献16

  • 1Yingshan ZHANG,Weiguo LI,Shisong MAO,Zhongguo ZHENG.A SIMPLE METHOD FOR CONSTRUCTING ORTHOGONAL ARRAYS BY THE KRONECKER SUM[J].Journal of Systems Science & Complexity,2006,19(2):266-273. 被引量:8
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二级参考文献13

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