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Hadamard matrices of order $$\equiv{} 8$$(mod 16) with maximal excess. (English) Zbl 0762.05024
The excess of a Hadamard matrix $$H$$, denoted $$\sigma(H)$$, is the sum of all its elements. $$\sigma(n)$$ is used to denote the maximal excess of all Hadamard matrices of order $$n$$. In this paper a new family of Hadamard matrices whose excess is maximal is given. It is shown that there is a Hadamard matrix of order $$4m(m-1)$$ $$(\equiv 0\pmod{16}$$ and $$\equiv 8\pmod{16}$$, respectively) whose excess meets the Kounias-Farmakis bound, i.e. $$\sigma(4m(m-1))=4(m-1)^ 2(2m+1)$$.

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
##### Keywords:
Hadamard matrices; maximal excess; Kounias-Farmakis bound
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