A210206 Maximal number of 1s in a Hadamard matrix of order 4n.

12, 42, 90, 160, 240, 344, 462, 598, 756, 922, 1108, 1314, 1534, 1772

Offset: 1

Author

N. J. A. Sloane, Mar 18 2012

Keywords

• nonn
• more

Comments

The weight of a {-1,1} matrix is defined to be the number of elements equal to 1. The excess is defined to be the sum of the matrix elements. The weight and excess of an N x N matrix are related by (weight) = (excess + N^2) / 2. Hence a(n) = (A004118+16n^2)/2. - William P. Orrick, Jun 25 2015

Links

• 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.

Crossrefs

Cf. A004118.

Extensions

a(5)-a(14) from William P. Orrick, Jun 25 2015

Farmakis & Kounias references added by William P. Orrick, Jun 25 2015