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An inner orthogonality of Hadamard matrices

Published online by Cambridge University Press:  09 April 2009

K. A. Bush
K. A. Bush
Affiliation:
Washington State University and The Australian National University
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We say a matrix H of order 4t is Hadamard if each entry is 1 or — 1, and the inner product of any two rows is zero. We shall consider only Hadamard matrices in normal form with the first row consisting solely of 1 while any two of the remaining rows have the property that hik = hjk = 1, hik = –hjk = 1, —hik = hjk = 1, and –hik = –hjk = 1 each occur t times. We can induce a further normalization by choosing the second row of H to have the first 2t entries 1 and the last 2t entries — 1, and this will be the standard form we consider. We now call the submatrix obtained by deleting the first two rows of H and the first It columns. H therefore is of dimension 4t — 2 x 2t. We prove the following theorem:

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 2 , May 1971 , pp. 242 - 248
Copyright
Copyright © Australian Mathematical Society 1971

References

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