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Generalized Hadamard matrices whose transposes are not generalized Hadamard matrices

✍ Scribed by R. Craigen; W. de Launey


Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
69 KB
Volume
17
Category
Article
ISSN
1063-8539

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✦ Synopsis


Abstract

In answer to β€œResearch Problem 16” in Horadam's recent book Hadamard matrices and their applications, we provide a construction for generalized Hadamard matrices whose transposes are not generalized Hadamard matrices. Β© 2009 Wiley Periodicals,
Inc. J Combin Designs 17: 456–458, 2009


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## Abstract We investigate signings of symmetric GDD($16 \times 2^i$, 16, $2^{4-i}$)s over $Z\_2$ for $1 \le i \le 3$. Beginning with $i=1$, at each stage of this process a signing of a GDD($16 \times 2^i$, 16, $2^{4-i}$) produces a GDD($16 \times 2^{i+1}$, 16, $2^{4-i-1}$). The initial GDDs ($i=1$