A Hadamard matrix $H$ is skew Hadamard if $H+H^{T}=2I$.

A collection of skew Hadamard matrices, including at least one example of every order $n\leq 100$ and also including every equivalence class of order $\leq 28$, is available http://www.rangevoting.org/SkewHad.htmlat this web page. It has been conjectured that one exists for every positive order divisible by 4.

Reid and Brown in 1972 showed that there exists a “doubly regular tournament of order n” if and only if there exists a skew Hadamard matrix of order n+1.

## References

• 1 S. Georgiou, C. Koukouvinos, J. Seberry, Hadamard matrices, orthogonal designs and construction algorithms, pp. 133-205 in DESIGNS 2002: Further computational and constructive design theory, Kluwer 2003.
• 2 K.B. Reid, E. Brown, Doubly regular tournaments are equivalent to skew Hadamard matrices, J. Combinatorial Theory A 12 (1972) 332-338.
• 3 J. Seberry, M.Yamada, Hadamard matrices, sequences, and block designs, pp. 431-560 in Contemporary Design Theory, a collection of surveys (J.H.Dinitz & D.R.Stinson eds.), Wiley 1992.
Title skew Hadamard matrix SkewHadamardMatrix 2013-03-22 16:13:02 2013-03-22 16:13:02 Mathprof (13753) Mathprof (13753) 13 Mathprof (13753) Definition msc 15-00