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

✍ Scribed by Christos Koukouvinos; Jennifer Seberry

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 237 KB
• Volume: 92
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90278-a

✦ Synopsis

Koukouvinos, C. and J. Seberry, Hadamard matrices of order =8(mod 16) with maximal excess, Discrete Mathematics 92 (1991) 173-176. 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, u(h) for h = 4m(m -1) is give,1 by o(4m(m -. 1)) < 4(m -1)'(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.