Cocyclic Hadamard matrices and difference sets

This paper locates cocyclic Hadamard matrices within the mainstream of combinatorial design theory. We prove that the existence of a cocyclic Hadamard matrix of order 4t is equivalent to the existence of a normal relative difference set with parameters (4t,2,4t,2t). In the basic case we note there i...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2000-05, Vol.102 (1), p.47-61
Main Authors: de Launey, Warwick, Flannery, D.L., Horadam, K.J.
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Group theory
Group theory and generalizations
Mathematics
Sciences and techniques of general use
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Summary:This paper locates cocyclic Hadamard matrices within the mainstream of combinatorial design theory. We prove that the existence of a cocyclic Hadamard matrix of order 4t is equivalent to the existence of a normal relative difference set with parameters (4t,2,4t,2t). In the basic case we note there is a corresponding equivalence between coboundary Hadamard matrices and Menon–Hadamard difference sets. These equivalences unify and explain results in the theories of Hadamard groups, divisible designs with regular automorphism groups, and periodic autocorrelation functions.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(99)00230-9