Showing papers on "Orthogonal array published in 1975"
TL;DR: In this paper, the authors obtained the best possible bound on the number of orthogonal F-squares with certain parameters and gave a construction method for some families of F-square which achieve this bound.
Abstract: : The main purpose of the paper is to obtain the best possible bound on the number of orthogonal F-squares with certain parameters and to give a construction method for some families of orthogonal F-squares which achieve this bound. Also, presented is a set of four mutually orthogonal F-squares of order 6 based on three symbols. This later design is important because there is no orthogonal Latin squares of order 6 which could be used for this purpose as has been pointed out by Hedayat and Seiden (1970). The authors indicate a method of composing orthogonal F-squares. It is shown under what condition a set of orthogonal F-squares can be transformed into an orthogonal array, a structure which is useful for factorial experimentation. (Modified author abstract)
48 citations
TL;DR: In this article, it was shown that orthogonal designs of type (1,k) and ordern exist for everyk < n whenn = 2t+2⋅3 andn = 1t+3⋆⋈5 (wheret is a positive integer), and that the orthogonality of these designs is a natural generalization of the Baumert-Hall arrays which have been used to construct Hadamard matrices.
Abstract: Orthogonal designs are a natural generalization of the Baumert-Hall arrays which have been used to construct Hadamard matrices. We continue our investigation of these designs and show that orthogonal designs of type (1,k) and ordern exist for everyk < n whenn = 2
t+2⋅3 andn = 2
t+2⋅5 (wheret is a positive integer). We also find orthogonal designs that exist in every order 2n and others that exist in every order 4n.
Coupled with some results of earlier work, this means that theweighing matrix conjecture ‘For every ordern ≡ 0 (mod 4) there is, for eachk ⩽n, a square {0, 1, − 1} matrixW = W(n, k) satisfyingWW
t
=kIn’ is resolved in the affirmative for all ordersn = 2t+1⋅3,n = 2t+1⋅5 (t a positive integer). The fact that the matrices we find are skew-symmetric for allk < n whenn ≡ 0 (mod 8) and because of other considerations we pose three other conjectures about weighing matrices having additional structure and resolve these conjectures affirmatively in a few cases. In an appendix we give a table of the known results for orders ⩽ 64.
19 citations
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01 Jan 1975
TL;DR: In this paper, it was shown that orthogonal designs of type (1, k) and order n exist for every k > n when n = 2t+2.3 and n = n 2t + 2.5 (where t is a positive integer).
Abstract: Orthogonal designs are a natural generalization of the Baumert-Hall arrays which have been used to construct Hadamard matrices. We continue our investigation of these designs and show that orthogonal designs of type (1, k) and order n exist for every k
2 citations
01 Jan 1975
TL;DR: In this paper, a class of nonsinusoidal orthogonal functions, which consists of Rademacher functions, Haar functions, and Walsh functions, is introduced, and a parameter called sequency is defined to distinguish individual functions belonging to such sets of functions.
Abstract: The purpose of this chapter is to introduce a class of nonsinusoidal orthogonal functions which consists of: (1) Rademacher functions, (2) Haar functions, and (3) Walsh functions. These orthogonal functions consist of either square or rectangular waves. Individual functions belonging to such sets of functions are distinguished by means of a parameter called sequency. Some aspects pertaining to notation for representing nonsinusoidal orthogonal functions are also discussed.