skew Hadamard matrix
A Hadamard matrix
H is skew Hadamard if H+HT=2I.
A collection of skew Hadamard matrices, including at least one example of every order n≤100
and also including every equivalence class
of order ≤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
-
3
J. Seberry, M.Yamada, Hadamard matrices, sequences, and block designs
| 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 |