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On the excess of Hadamard matrices. (English) Zbl 0667.05013
Bounds for the excess $$\sigma$$ (H) of a Hadamard matrix H the sum of the elements of the matrix H, are established in the work. $$\sigma$$ (n) denotes the maximum of $$\sigma$$ (H) for all Hadamard matrices of order n. Upper bounds for $$\sigma$$ (n), with n from various intervals, are obtained, improving the well-known bound $$n\sqrt{n}$$. The established bound coincides with $$n\sqrt{n}$$ when $$n=(4m)^ 2$$ or $$n=4(2m+1)^ 2$$ and the matrix H is regular, i.e. it has all row and column sums equal.
Regular matrices are constructed for $$n=4(2m+1)^ 2$$ when $$m=1,2,3$$ and their construction for $$m=4,9,12$$ is indicated. A procedure is described to find all row-sum and column-sum vectors of a Hadamard matrix with given excess.
Reviewer: S.S.Agayan

##### MSC:
 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
##### Keywords:
H-matrix; excess of Hadamard matrix
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##### References:
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