A158863
Maximal excess of a 3-normalized Hadamard matrix of order 4n.
Original entry on oeis.org
4, 8, 36, 32, 76, 72, 124, 128, 180, 200, 244, 288, 316
Offset: 1
A158865
Smallest maximal excess attained by an equivalence class of Hadamard matrices of order 4n.
Original entry on oeis.org
0, 8, 20, 36, 56, 80, 108, 140
Offset: 0
All equivalence classes in orders 20 and 28 attain the same maximal excess. In order 16, three classes attain maximal excess 64 and two attain maximal excess 56. In order 24, 56 equivalence classes attain maximal excess 112 and four attain maximal excess 108.
- Best, M. R. The excess of a Hadamard matrix. Nederl. Akad. Wetensch. Proc. Ser. A {80}=Indag. Math. 39 (1977), no. 5, 357-361.
- Brown, Thomas A. and Spencer, Joel H., Minimization of +-1 matrices under line shifts. Colloq. Math. 23 (1971), 165-171, 177 (errata).
- R. Craigen and H. Kharaghani, Weaving Hadamard matrices with maximum excess and classes with small excess. J. Combinatorial Designs 12 (2004), 233-255.
A210206
Maximal number of 1s in a Hadamard matrix of order 4n.
Original entry on oeis.org
12, 42, 90, 160, 240, 344, 462, 598, 756, 922, 1108, 1314, 1534, 1772
Offset: 1
- Thomas A. Brown and Joel H. Spencer, Minimization of +-1 matrices under line shifts Colloq. Math. 23 (1971), 165-171, 177 (errata).
- N. Farmakis and S. Kounias, The excess of Hadamard matrices and optimal designs, Discrete Mathematics, 67 (1987), 165-176.
- S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics, 68 (1988), 59-69.
- K. W. Schmidt, Edward T. H. Wang, The weights of Hadamard matrices. J. Combinatorial Theory Ser. A 23 (1977), no. 3, 257--263. MR0453564 (56 #11826)
- N. J. A. Sloane, Hadamard matrices, gives representatives of all Hadamard matrix equivalence classes for sizes up to 28, and a representative of at least one equivalence class for sizes up to 256. Most are not of maximal weight, however.
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