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Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18 | Masaaki Harada
; Clement Lam
; Akihiro Munemasa
; Vladimir D. Tonchev
; | Date: |
15 Jul 2010 | Abstract: | 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). | Source: | arXiv, 1007.2555 | Services: | Forum | Review | PDF | Favorites |
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