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Criteria for a Hadamard Matrix to be Skew-Equivalent

Published online by Cambridge University Press:  20 November 2018

Judith Q. Longyear
Judith Q. Longyear*
Affiliation:
Wayne State University, Detroit, Michigan
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A matrix H of order n = 4t with all entries from the set ﹛1, —1﹜ is Hadamard if HHt = 4tI. The set of Hadamard matrices is . A matrix is of type I or is skew-Hadamard if H = S — I where St = —S (some authors also use H = S + I). The set of type I members is . A matrix P is a signed permutation matrix if each row and each column has exactly one non-zero entry, and that entry is from the set ﹛1, —1﹜.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1216 - 1223
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Hall, M., Jr. Hadamard matrices of order 16, J.P.L. Research summary No. 36-10, 1 (1961), 21–26.Google Scholar
2. Hall, M., Jr. Note on the Matthieu group Mu, Arch. Math. 13 (1962), 334–340.Google Scholar
3. Hall, M., Jr. Hadamard matrices of order 20, J.P.L. Technical Report No. 32-761 (1965), 1–41.Google Scholar
4. Hall, M., Jr. Combinatorial theory (Ginn-Blaisdell, Waltham, Mass., 1967).Google Scholar
5. Johnson, E. C., Skew-Hadamard abelian group difference sets, J. Algebra 1 (1964), 388–402.Google Scholar