On twin prime power Hadamard matrices

O Cathain, Padraig and Stafford, Richard M. (2010) On twin prime power Hadamard matrices. Cryptography and Communications, 2 2: 261-269. doi:10.1007/s12095-010-0030-2


Author O Cathain, Padraig
Stafford, Richard M.
Title On twin prime power Hadamard matrices
Journal name Cryptography and Communications   Check publisher's open access policy
ISSN 1936-2447
1936-2455
Publication date 2010-09
Sub-type Article (original research)
DOI 10.1007/s12095-010-0030-2
Volume 2
Issue 2
Start page 261
End page 269
Total pages 9
Place of publication New York, USA
Publisher Springer New York
Language eng
Abstract In this paper, we show that exactly one Hadamard matrix constructed using the twin prime power method is cocyclic. We achieve this by showing that the action of the automorphism group of a Hadamard matrix developed from a difference set induces a 2-transitive action on the rows of the matrix or is intransitive. We then use Ito’s classification of Hadamard matrices with 2-transitive automorphism groups to derive a necessary condition on the order of a cocyclic Hadamard matrix developed from a difference set. This work answers a research problem posed by K.J. Horadam, and exhibits the first known infinite family of Hadamard matrices which are not cocyclic.
Keyword Hadamard matrix
Cocyclic
Twin prime powers
2-transitive action
Primary 05B20.05E18
Secondary 20B20
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 06 Nov 2013, 12:31:37 EST by Kay Mackie on behalf of School of Mathematics & Physics