Geodesic
Classification of generalized Hadamard matrices \(H(6,3)\) and quaternary Hermitian self-dual codes of length 18
The electronic journal of combinatorics, Tome 17 (2010)
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All generalized Hadamard matrices of order 18 over a group of order 3, $H(6,3)$, are enumerated in two different ways: once, as class regular symmetric $(6,3)$-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual $[18,9]$ codes over $GF(4)$, completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices $H(6,3)$, and 245 inequivalent Hermitian self-dual codes of length 18 over $GF(4)$.
DOI : 10.37236/443
Classification : 05B20, 94B05
Mots-clés : generalized Hadamard matrix 
@article{10_37236_443,
     author = {Masaaki Harada and Clement Lam and Akihiro Munemasa and Vladimir D. Tonchev},
     title = {Classification of generalized {Hadamard} matrices {\(H(6,3)\)} and quaternary {Hermitian} self-dual codes of length 18},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/443},
     zbl = {1204.05032},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/443/}
}
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Masaaki Harada; Clement Lam; Akihiro Munemasa; Vladimir D. Tonchev. Classification of generalized Hadamard matrices \(H(6,3)\) and quaternary Hermitian self-dual codes of length 18. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/443

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