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Constructions for amicable orthogonal designs

Published online by Cambridge University Press:  17 April 2009

Jennifer Seberry Wallis
Jennifer Seberry Wallis
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Infinite families of amicable orthogonal designs are constructed with

(i) both of type (1, q) in order q + 1 when q ≡ 3 (mod 4) is a prime power,

(ii) both of type (1, q) in order 2(q + 1) where q ≡ 1 (mod 4) is a prime power or q + 1 is the order of a conference matrix,

(iii) both of type (2, 2q) in order 2(q + 1) when q ≡ 1 (mod 4) is a prime power or q + 1 is the order of a conference matrix.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 2 , April 1975 , pp. 179 - 182
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Geramita, Anthony V., Geramita, Joan Murphy, Wallis, Jennifer Seberry, “Orthogonal designs”, J. Lin. Multilin. Algebra (to appear).Google Scholar
[2]Wallis, Jennifer Seberry, “Hadamard matrices”, Combinatorics: Room squares, sum-free sets, Hadamard matrices, 273–489 (Lecture Notes in Mathematics, 292. Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[3]Wolfe, Warren W., “Clifford algebras and amicable orthogonal designs”, Queen's Mathematical Preprint No. 1974–22.Google Scholar