Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T14:15:00.529Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-automorphisms of Hadamard matrices

Published online by Cambridge University Press:  24 October 2008

Marshall Hall Jr
Marshall Hall Jr
Affiliation:
California Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Extract

A Hadamard matrix Hn is an n by n matrix H = [hij], i, j = 1, …, n in which every entry hij is + 1 or − 1, such that

It is well known that possible orders are n = 1, 2 and n = 4m. An automorphism α of H is given by a pair P, Q of monomial ± 1 matrices such that

Here P permutes and changes signs of rows, while Q acts similarly on columns.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 77 , Issue 3 , May 1975 , pp. 459 - 473
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Assmus, E. F. Jr and Mattson, H. F. JrNew 5-designs. J. Comb. Theory 6 (1969), 122–151.Google Scholar
(2)Conway, J. H.A Group of order 8, 315, 553, 613, 086, 720, 000. Bull. London Math. Soc. 1 (1969), 79–88.Google Scholar
(3)Hall, Marshall Jr, Note on the Mathieu Group M 12. Archiv der Mathematik 13 (1962), 334–340.Google Scholar
(4)Marshall, Hall Jr, Combinatorial theory. Blaisdell Publishing Co. (Waltham, Massachusetts 1967.)Google Scholar
(5)Kantor, William M.Automorphism groups of Hadamard matrices. J. Comb. Theory 6 (1969), 297–281.Google Scholar
(6)Pless, Vera. Symmetry codes over GF(3) and new five-designs. J. Comb. Theory 12 (1972), 119–142.Google Scholar