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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.)
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