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, o(h) for h = 4m(m -1) is given by
o(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.
Publication Details
Christos Koukouvinos and Jennifer Seberry, Hadamard matrices of order ? (8 mod 16) with maximal excess, Discrete Mathematics, 92, (1991), 173-176, also appeared in Selected Papers in Combinatorics - a Volume Dedicated to R.G. Stanton, Topics in Discrete Mathematics, 2, North Holland, New York, 1992.