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Hadamard Matrices and Dihedral Groups
Authors:Hiroshi Kimura
Affiliation:(1) Department of Mathematics, Ehime University, 790-77 Matsuyama, Japan
Abstract:
Let D2p be a dihedral group of order 2p, where p is an odd integer. Let ZD2p be the group ring of D2p over the ring Z of integers. We identify elements of ZD2p and their matrices of the regular representation of ZD2p. Recently we characterized the Hadamard matrices of order 28 ([6] and [7]). There are exactly 487 Hadamard matrices of order 28, up to equivalence. In these matrices there exist matrices with some interesting properties. That is, these are constructed by elements of ZD6. We discuss relation of ZD2p and Hadamard matrices of order n=8p+4, and give some examples of Hadamard matrices constructed by dihedral groups.
Keywords:Dihedral groups  Hadamard matrices
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