Corpus ID: 115911196

Hadamard matrices, Sequences, and Block Designs

@inproceedings{Seberry1992HadamardMS,
  title={Hadamard matrices, Sequences, and Block Designs},
  author={J. Seberry and Mieko Yamada},
  year={1992}
}
One hundred years ago, in 1893, Jacques Hadamard [31] found square matrices of orders 12 and 20, with entries ±1, which had all their rows (and columns) pairwise orthogonal. These matrices, X = (Xij), satisfied the equality of the following inequality, |detX|2 ≤ ∏ ∑ |xij|2, and so had maximal determinant among matrices with entries ±1. Hadamard actually asked the question of finding the maximal determinant of matrices with entries on the unit disc, but his name has become associated with the… Expand
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References

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An Hadamard matrix H is a. square matrix of ones and minus ones whose row (and hence column) vectors are orthogonal. The order n of an Hadamard matrix is necessarily 1, 2 or At with / = 1, 2, 3, • •Expand
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Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and Williamson-type matrices. These latter are four (1,-1) matrices A,B,C,D, of order m,Expand
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Recent advances in the construction of Hadamard matrices have depended on the existence of Baumert-Hall arrays and four (1,-1) matrices A, B, C, D of order m which are of Williamson type; that is,Expand
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A 4n x 4n Hadamard array, H, is a square matrix of order 4n with elements ± A, ± B, ± C, ± D each repeated n times in each row and column. Assuming the indeterminates A, B, C, D commute, the rowExpand
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Recently I have proved that for every odd integer q there exists integers t and s (dependent on q) so that there is an Hadamard matrix of order 2tq and a symmetric Hadamard matrix with constantExpand
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If a (*)-type Hadamard matrix of order 2n (i.e. a pair (A, B) of n X n circulant (1, 1) matrices satisfying AA' + BB' = 2nI) exists and a pair of Golay complementary sequences (or equivalently,Expand
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