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Construction of some Hadamard matrices with maximum excess. (English) Zbl 0732.05016
Let H be an Hadamard matrix of order n. Then the sum of the elements of H is called the excess $$\sigma$$ (H) of H. Moreover $$\sigma$$ (n) denotes the maximum of all $$\sigma$$ (H), where H runs over all Hadamard matrices of order n.
In the previous paper [Discrete Math. 68, 59-69 (1988; Zbl 0667.05013)] the authors gave an upper bound k(n) for some values of n including 10 values given below. Now in the present paper the authors determine $$\sigma$$ (n) by constructing Hadamard matrices H with $$\sigma (H)=k(n)$$ for the following 10 values of n: $$\sigma (228)=3420$$, $$\sigma (364)=6916$$; $$\sigma (532)=12236$$; $$\sigma (1092)=36036$$; $$\sigma (1764)=74088$$; $$\sigma (2604)=132804$$; $$\sigma (2812)=149036$$; $$\sigma (4356)=287496$$; $$\sigma (5332)=389236$$ and $$\sigma (5476)=405224$$.

MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)