Geodesic
Limits on Pairwise Amicable Orthogonal Designs
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1043-1054

Voir la notice de l'article provenant de la source Cambridge University Press

An orthogonal design in order n of type (u 1, ..., ut ) on the commuting variables x 1, ..., xt is an n × n matrix X with entries 0, ±x 1, ..., ±xt such that In [5] Geramita and Wallis show that if n = 24a+b ·n 0, where n 0 is odd and 0 ≦ b > 4, then t ≧ ρ(n) = 8a + 2b. The result is essentially Radon's limit on the number of anti-commuting, real, anti-symmetric, orthogonal matrices in order n. Garamita and Pullman show that this limit is sharp for orthogonal designs: i.e., given n, there exists an orthogonal design in order n with ρ(n) variables [6].Two orthogonal designs, X and F, are called amicable if XYt = YXt.Such pairs of orthogonal designs are especially useful in generating new orthogonal designs [5] or [6]. 
Wolfe, Warren. Limits on Pairwise Amicable Orthogonal Designs. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1043-1054. doi: 10.4153/CJM-1981-079-x
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