skew Hadamard matrix
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 $n\le 100$ and also including every equivalence class^{} of order $\le 28$, 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 |
---|---|
Canonical name | SkewHadamardMatrix |
Date of creation | 2013-03-22 16:13:02 |
Last modified on | 2013-03-22 16:13:02 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 13 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 15-00 |