Abstract
Let D 2p be adihedral group of order 2p, where pis an odd integer. Let Z D 2p be the group ringof D 2p over the ring Z of integers.We identify elements of Z D 2p and their matricesof the regular representation of Z D 2p . Recently we characterized the Hadamard matrices of order 28 ([6]) and ([7]). There are exactly 487 Hadamardmatrices of order 28, up to equivalence. In thesematrices there exist matrices with some interesting properties.That is, these are constructed by elements of ZD 6.We discuss relation of Z D 2p and Hadamard matricesof order n=8p+4, and give some examples of Hadamardmatrices constructed by dihedral groups.
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Kimura, H. Hadamard Matrices and Dihedral Groups. Designs, Codes and Cryptography 9, 71–77 (1996). https://doi.org/10.1023/A:1027342024177
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DOI: https://doi.org/10.1023/A:1027342024177