Hostname: page-component-54dcc4c588-wlffp Total loading time: 0 Render date: 2025-09-12T17:27:11.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Group properties of Hadamard matrices

Published online by Cambridge University Press:  09 April 2009

Marshall Hall Jr
Marshall Hall Jr
Affiliation:
Department of MathematicsCalifornia Institute of Technology Pasadena, California, U.S.A.
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.

An Hadamard matrix H is a square matrix of order n all of whose entries are ± 1 such thatThere are matrices of order 1 and 2and for all other Hadamard matrices the order n is a multiple of 4, n = 4m. It is a reasonable conjecture that Hadamard matrices exist for every order which is a multiple of 4 and the lowest order in doubt is 268. With every Hadamard matrix H4m a symmetric design D exists with

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 247 - 256
Copyright
Copyright © Australian Mathematical Society 1976

References

Baumert, L. D. (1971), Cyclic difference sets (Lecture notes in Mathematics No. 182, Springer, Berlin-New York).CrossRefGoogle Scholar
Baumert, L. D. and Hall, Marshall Jr (1965), ‘A new construction for Hadamard matrices’, Bull. Amer. Math. Soc. 71, 169–170.CrossRefGoogle Scholar
Hall, Marshall Jr (1962), ‘A note on the Mathieu group M12’, Arch. Math (Basel) 13, 334–340.CrossRefGoogle Scholar
Hall, Marshall Jr (1967), Combinatorial theory (Blaisdell, Walham, Massachusetts, 1967).Google Scholar
Hall, Marshall Jr (to appear), ‘Semi-automorphisms of Hadamard matrices’, Proc. Cambridge Philos. Soc.Google Scholar
Higman, D. G. (1964), ‘Finite permutation groups of rank 3’, Math. Z. 86, 145–156.CrossRefGoogle Scholar
Kantor, William (1969), ‘Automorphism groups of Hadamard matrices’, J. Combinatorial Theory 6, 279–281.CrossRefGoogle Scholar
Kantor, William (to appear), ‘Symplectic groups, symmetric designs and line ovals’, J. Combinatorial Theory.Google Scholar
Norman, Christopher (1968), ‘A characterization of the Mathieu group M11’, Math. Z. 106, 162–166.CrossRefGoogle Scholar
Pless, Vera (1972), ‘Symmetry codes over GF(3) and new Five-designs’, J. Combinatorial Theory 12, 119–142.CrossRefGoogle Scholar
Turyn, R. J. (1974), ‘Hadamard matrices, Baumert-Hall units, four symbol sequences, pulse compression, and surface wave encodings’, J. Combinatorial Theory 16, 313–333.CrossRefGoogle Scholar
Turyn, R. J. (1972), ‘An infinite class of Williamson matrices’, J. Combinatorial Theory 12, 219–321.CrossRefGoogle Scholar
Wallis, Jennifer (1973), ‘Hadamard matrices of order 28m, 36m, and 44m’, J. Combinatorial Theory 15, 323–328.CrossRefGoogle Scholar
Williamson, J. (1944), ‘Hadamard's determinant theorem and the sum of four squares’, Duke Math. J. 11, 65–81.CrossRefGoogle Scholar