A158863 Maximal excess of a 3-normalized Hadamard matrix of order 4n.

4, 8, 36, 32, 76, 72, 124, 128, 180, 200, 244, 288, 316

Offset: 1

Author

William P. Orrick, Mar 28 2009

Keywords

• hard
• more
• nonn

Comments

The excess of a {-1,1} matrix is the sum of its elements. A Hadamard matrix is 3-normalized if its first three rows contain an even number of entries -1 in each column. 3-normalized Hadamard matrices of order 4n with large excess can be used to construct large-determinant {-1,1} matrices of order 4n+1.

Links

• W. P. Orrick and B. Solomon, The Hadamard Maximal Determinant Problem (website)
• W. P. Orrick and B. Solomon, Large-determinant sign matrices of order 4k+1, Discr. Math. 307 (2007), 226-236.

Crossrefs

Cf. A004118.