Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-29T16:51:44.650Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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