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Orthogonal arrays obtained by generalized difference matrices with g levels

Science China Mathematics 2011年第1期54卷 133-143页

作者： ZHANG YingShan LI WeiGuo MAO ShiSong ZHENG ZhongGuo School of Finance and Statistics East China Normal University Shanghai 200241 China School of Sciences Beijing University of Aeronautics and Astronautics Beijing 100083 China Lab of Mathematics and Its Application Peking University Beijing 100871 China

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.

关键词： mixed-level orthogonal arrays generalized difference matrices projection matrices permutation matrices

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A Family of Asymmetrical Orthogonal Arrays with Run Sizes 4p^2

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Chinese Quarterly Journal of Mathematics 2007年第3期22卷 426-435页

作者：廖靖宇张建军张应山 Department of Mathematics Xuchang College Department of Statistics East China Normal University

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.

关键词： mixed-level orthogonal arrays generalized difference matrices projective matrices permutable matrices

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