Construction of some Hadamard matrices with maximum excess

AbstractLet σ(n) be the maximum excess of an Hadamard matrix of order n. Hadamard matrices with maximum excess are constructed for the following cases: (i) n = (4m + 1)2 + 3 for m = 8, 13, 18 with σ(n) = n(4m + 1) = nn − 3, (ii) n = (4m + 3)2 + 3 for m = 3, 4, 5, 12 with σ(n) = n(4m + 3) = nn − 3, (iii) n = 4(2m + 1)2 for m = 10, 16, 18 with σ(n) = n(4m + 2) = nn

CONSTRUCTION OF SOME HADAMARD-MATRICES WITH MAXIMUM EXCESS

Let sigma(n) be the maximum excess of an Hadamard matrix of order n. Hadamard matrices with maximum excess are constructed for the following cases: (i) n = (4m+1)2+3 for m = 8, 13, 18 with sigma(n) = n(4m+1) = n square-root n-3, (ii) n = (4m+3)2+3 for m = 3, 4, 5, 12 with sigma(n) = n(4m+3) = n square-root n-3, (iii) n = 4(2m+1)2 for m = 10, 16, 18 with sigma(n) = n(4m+2) = n square-root n