Graphs and Combinatorics

, Volume 5, Issue 1, pp 235–242

New Hadamard matrix of order 24

  • Hiroshi Kimura
Article

Abstract

In this paper we give a new Hadamard matrix of order 24 and its properties. This matrix must be appear in [11]. By this paper and Ito-Leon-Longyear [3] the classification of Hadamard matrices of order 24 is completed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hall, M. Jr.: Combinatorial Theory. Boston: Ginn (Blaisdell) 1967Google Scholar
  2. 2.
    Ito, N., Leon, J.S., Longyear, J.Q.: The 24-dimensional Hadamard matrices and their automorphism groups (unpublished)Google Scholar
  3. 3.
    Ito, N., Leon, J.S., Longyear, J.Q.: Classification of 3-(24, 12, 5) designs and 24-dimensional Hadamard matrices. J. Comb. Theory (A)27, 289–306 (1979)Google Scholar
  4. 4.
    Kimura, H.: Hadamard matrices of order 28 with automorphism groups of order two. J. Comb. Theory (A)43, 98–102 (1986)Google Scholar
  5. 5.
    Kimura, H.: On equivalence of Hadamard matrices. Hokkaido Math. J.17, 139–146 (1988)Google Scholar
  6. 6.
    Kimura, H.: Table ofH-matrices and K-boxes of order 24 (unpublished)Google Scholar
  7. 7.
    Kimura, H., Ohmori, H.: Construction of Hadamard matrices of order 28. Graphs and Combinatorics2, 247–257 (1986)Google Scholar
  8. 8.
    Kimura, H., Ohmori, H.: Hadamard matrices of order 28. Memoirs of the Faculty of Education, Ehime Univ.7, 7–57 (1987)Google Scholar
  9. 9.
    Leon, J.S.: An algorithm for computing the automorphism group of a Hadamard matrix. J. Comb. Theory (A)27, 287–306 (1979)Google Scholar
  10. 10.
    Longyear, J.Q.: There is one Hadamard matrix of order 24 and both characters 1. Second International Conference on Combinatorial Mathematics. Annals of the New York Academy of Science319, 354–361 (1979)Google Scholar
  11. 11.
    Longyear, J.Q.: If a Hadamard of order 24 has character exactly 2, its transpose is known, in Theory and Applications of Groups. Lect. Notes Math.642, 353–363, (1978)Google Scholar
  12. 12.
    Longyear, J.Q.: Order 24 Hadamard matrices of character at least 3. J. Comb. Theory (A)27, 100–118 (1979)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Hiroshi Kimura
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceEhime UniversityMatsuyamaJapan

Personalised recommendations