On the excess of Hadamard matrices

Abstract Let σ ( n ) be the maximum excess of an Hadamard matrix of order n . Improved upper bounds are given for σ ( n ) and a procedure is described to find all row-sum or column-sum vectors of an Hadamard matrix with given excess. Hadamard matrices with maximum excess are constructed for n =124, 172, 196 and n =4(2 m + 1) 2 for certain values of m .

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