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Enumeration of generalized Hadamard matrices of order 16 and related designs

✍ Scribed by P. B. Gibbons; R. Mathon

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 142 KB
Volume: 17
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20193

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✦ Synopsis

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 ($i=1$) correspond to Hadamard matrices of order 16. For $i=3$, the GDDs are semibiplanes of order 16, and for $i=4$ the GDDs are semiplanes of order 16 which can be extended to projective planes of order 16. In this article, we completely enumerate such signings which include all generalized Hadamard matrices of order 16. We discuss the generation techniques and properties of the designs obtained during the search. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 119–135, 2009

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