Orthogonal arrays obtained by generalized difference matrices with g levels  

作　　者：ZHANG YingShan LI WeiGuo MAO ShiSong ZHENG ZhongGuo 

机构地区：[1]School of Finance and Statistics, East China Normal University, Shanghai 200241, China [2]School of Sciences, Beijing University of Aeronautics and Astronautics, Beijing 100083, China [3]Lab of Mathematics and Its Application, Peking University, Beijing 100871, China

出　　处：《Science China Mathematics》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)

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.

关 键 词：mixed-level orthogonal arrays generalized difference matrices projection matrices permutation matrices 

分 类 号：O212.6[理学—概率论与数理统计] TP391.41[理学—数学]