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Hadamard matrices of order ¿8 (mod 16) with maximal excess

Journal Article


Abstract


  • Kounias and Farmakis, in 'On the excess of Hadamard matrices', Discrete Math. 68 (1988) 59-69, showed that the maximal excess (or sum of the elements) of an Hadamard matrix of order h, σ(h) for h = 4m(m - 1) is given by σ(4m(m - 1)) ≤ 4(m - 1)2(2m + 1). Kharaghani in 'An infinite class of Hadamard matrices of maximal excess' (to appear) showed this maximal excess can be attained if m is the order of a skew-Hadamard matrix. We give another proof of Kharaghani's result, by generalizing an example of Farmakis and Kounias, 'The excess of Hadamard matrices and optimal designs', Discrete Math. 67 (1987) 165-176, and further show that the maximal excess of the bound is attained if m ≡ 2 (mod 4) is the order of a conference matrix. © 1991.

Publication Date


  • 1991

Citation


  • Koukouvinos, C., & Seberry, J. (1991). Hadamard matrices of order ¿8 (mod 16) with maximal excess. Discrete Mathematics, 92(1-3), 173-176. doi:10.1016/0012-365X(91)90278-A

Scopus Eid


  • 2-s2.0-44949273119

Web Of Science Accession Number


Start Page


  • 173

End Page


  • 176

Volume


  • 92

Issue


  • 1-3

Abstract


  • Kounias and Farmakis, in 'On the excess of Hadamard matrices', Discrete Math. 68 (1988) 59-69, showed that the maximal excess (or sum of the elements) of an Hadamard matrix of order h, σ(h) for h = 4m(m - 1) is given by σ(4m(m - 1)) ≤ 4(m - 1)2(2m + 1). Kharaghani in 'An infinite class of Hadamard matrices of maximal excess' (to appear) showed this maximal excess can be attained if m is the order of a skew-Hadamard matrix. We give another proof of Kharaghani's result, by generalizing an example of Farmakis and Kounias, 'The excess of Hadamard matrices and optimal designs', Discrete Math. 67 (1987) 165-176, and further show that the maximal excess of the bound is attained if m ≡ 2 (mod 4) is the order of a conference matrix. © 1991.

Publication Date


  • 1991

Citation


  • Koukouvinos, C., & Seberry, J. (1991). Hadamard matrices of order ¿8 (mod 16) with maximal excess. Discrete Mathematics, 92(1-3), 173-176. doi:10.1016/0012-365X(91)90278-A

Scopus Eid


  • 2-s2.0-44949273119

Web Of Science Accession Number


Start Page


  • 173

End Page


  • 176

Volume


  • 92

Issue


  • 1-3