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Decomposition of Hadamard matrices

✍ Scribed by Morris Plotkin

Publisher: Elsevier Science
Year: 1972
Tongue: English
Weight: 146 KB
Volume: 13
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(72)90015-5

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Let bp(+K v ) be the minimum number of complete bipartite subgraphs needed to partition the edge set of +K v , the complete multigraph with + edges between each pair of its v vertices. Many papers have examined bp(+K v ) for v 2+. For each + and v with v 2+, it is shown here that if certain Hadamard

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## Abstract In answer to “Research 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. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 456–458, 2009

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✍ D.L. Flannery 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 344 KB

In this paper, we prove that the concepts of cocyclic Hadamard matrix and Hadamard group are equivalent. A general procedure for constructing Hadamard groups and classifying such groups on the basis of isomorphism type is given. To illustrate the ideas, cocyclic Hadamard matrices over dihedral group

Automorphisms of higher-dimensional Hada

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✍ Warwick de Launey; Richard M. Stafford 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 308 KB

## Abstract This article derives from first principles a definition of equivalence for higher‐dimensional Hadamard matrices and thereby a definition of the automorphism group for higher‐dimensional Hadamard matrices. Our procedure is quite general and could be applied to other kinds of designs for

Checkered Hadamard Matrices of Order 16

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In this paper all the so-called checkered Hadamard matrices of order 16 are determined (i.e., Hadamard matrices consisting of 16 square blocks H i j of order 4 such that H ii = J 4 and H i j J 4 = J 4 H i j = 0 for i = j and where J 4 is the all-one matrix of order 4). It is shown that the checkered