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Arrays for orthogonal designs
Author(s) -
Kharaghani H.
Publication year - 2000
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(2000)8:3<166::aid-jcd2>3.0.co;2-r
Subject(s) - circulant matrix , orthogonal array , mathematics , combinatorics , set (abstract data type) , permutation (music) , permutation matrix , combinatorial design , orthogonal matrix , square (algebra) , discrete mathematics , arithmetic , computer science , orthogonal basis , taguchi methods , statistics , physics , acoustics , programming language , geometry , quantum mechanics
A set $\{A_1,A_2,\ldots ,A_{2n}\}$ of square real matrices is said to be amicable if$$\sum_{i=1}^n (A_{\sigma (2i-1)} A_{\sigma (2i)}^t - A_{\sigma (2i)} A_{\sigma (2i-1)}^t)=0$$for some permutation σ of the set $\{1,2,\ldots ,2n\}$ . An infinite number of arrays which are suitable for any amicable set of eight circulant matrices are introduced. Applications include new classes of orthogonal designs. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 166–173, 2000