On maximal weights of Hadamard matrices |
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Authors: | Hikoe Enomoto Masahiko Miyamoto |
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Affiliation: | Department of Information Science, Faculty of Science, University of Tokyo, Tokyo, Japan;Department of Mathematics, Hokkaido University, Sapporo, Japan |
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Abstract: | Let denote the set of all Hadamard matrices of order n. For , define the weight of H to be the number of 1's in H and is denoted by w(H). For a subset , define the maximal weight of Γ as w(Γ) = max{w(H) | H?Γ}. Two Hadamard matrices are equivalent if one of them can be transformed to the other by permutation and negation of rows and columns, and the equivalence class containing H is denoted by [H]. In this paper, we shall derive lower bounds for w([H]), which are best possible for n ? 20. We shall also determine the exact value of . |
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