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 $n\\leq 100$ and also including every equivalence class of order $\\leq 28$ , is availablehttp://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.

单词	SkewHadamardMatrix
释义	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 $n\\leq 100$ and also including every equivalence class of order $\\leq 28$ , is availablehttp://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.
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