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Generalized Hadamard Matrices and Orthogonal Arrays of Strength Two

Published online by Cambridge University Press:  20 November 2018

S. S. Shrikhande
S. S. Shrikhande*
Affiliation:
University of Bombay
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The purpose of this note is to point out some connexions between generalized Hadamard matrices (4, 5) and various tactical configurations such as group divisible designs (3), affine resolvable balanced incomplete block designs (1), and orthogonal arrays of strength two (2). Some constructions for these arrays are also indicated.

A balanced incomplete block design (BIBD) with parameters v, b, r, k, λ is an arrangement of v symbols called treatments into b subsets called blocks of k < v distinct treatments such that each treatment occurs in r blocks and any pair of treatments occurs in λ blocks.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 736 - 740
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bose, R. C., A note on the resolvability of balanced incomplete block designs, Sankhyā, 6 (1942), 105–110.Google Scholar
2. Bose, R. C. and Bush, K. A., Orthogonal arrays of strength two and three, Ann. Math. Stat., 23 (1952), 508–524.Google Scholar
3. Bose, R. C. and Shimamoto, T., Classification and analysis of partially balanced incomplete block designs with two associate classes, J. Amer. Stat. Ass., 4-7 (1952), 151–184.Google Scholar
4. Butson, A. T., Generalized Hadamard matrices, Proc. Amer. Math. Soc, 13 (1962), 894–898.Google Scholar
5. Butson, A. T., Relations among generalized Hadamard matrices, Can. J. Math., 15 (1963), 42–48.Google Scholar
6. Kempthorne, O. and Addelman, S., Some main effect plans and orthogonal arrays of strength two, Ann. Math. Stat., 32 (1961), 1167–1178.Google Scholar
7. Plackett, R. L. and Burman, J. P., Designs of optimum multifactorial experiments, Biometrika, 33 (1946), 305–325.Google Scholar
8. Shrikhande, S. S., On the nonexistence of affine resolvable balanced incomplete block designs, Sankhyâ, 11 (1951), 185–186.Google Scholar
9. Shrikhande, S. S., On the dual of some balanced incomplete block designs, Biometrics, 8 (1952), 66–72.Google Scholar