Singly-even self-dual codes and Hadamard matrices

  • Masaaki Harada
  • Vladimir D. Tonchev
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 948)


A construction of binary self-dual singly-even codes from Hadamard matrices is described. As an application, all inequivalent extremal singly-even [40,20,8] codes derived from Hadamard matrices of order 20 are enumerated.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E.F. Assmus, Jr., and H.F. Mattson, Jr., New 5-designs, J. Combin. Theory 6 (1969), 122–151.Google Scholar
  2. 2.
    F.C. Bussemaker and V.D. Tonchev, New extremal doubly-even codes of length 56 derived from Hadamard matrices of order 28, Discrete Math. 76 (1989), 45–49.Google Scholar
  3. 3.
    F.C. Bussemaker and V.D. Tonchev, Extremal doubly-even codes of length 40 derived from Hadamard matrices of order 20, Discrete Math. 82 (1990), 317–321.Google Scholar
  4. 4.
    S. Buyuklieva and V. Yorgov, Singly-even dual codes of length 40, Proc. ACCT4 '94, Novgorod, Russia, 1994, 60–61.Google Scholar
  5. 5.
    P.J. Cameron and J.H. van Lint, Graphs, Codes and Designs, Cambridge University Press, Cambridge, 1980.Google Scholar
  6. 6.
    J.H. Conway and N.J.A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE. Trans. Inform. Theory 36 (1990), 1319–1333.Google Scholar
  7. 7.
    M. Hall, Jr., Hadamard matrices of order 20, Jet Propulsion Laboratory Technical Report No. 32–761, 1965.Google Scholar
  8. 8.
    M. Harada, Weighing matrices and self-dual codes, Ars Combinatoria, (to appear).Google Scholar
  9. 9.
    H. Kimura, Extremal doubly even (56,28,12) codes and Hadamard matrices of order 28, Australasian J. Combin. 10 (1994), 153–161. to appear.Google Scholar
  10. 10.
    F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.Google Scholar
  11. 11.
    V.D. Tonchev, Combinatorial Configurations, Longman Scientific and Technical, Wiley, New York, 1988.Google Scholar
  12. 12.
    V.D. Tonchev, Self-orthogonal designs and extremal doubly-even codes, J. Combin. Theory Ser. A 52 (1989), 197–205.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Masaaki Harada
    • 1
  • Vladimir D. Tonchev
    • 2
  1. 1.Department of MathematicsOkayama UniversityOkayamaJapan
  2. 2.Mathematical SciencesMichigan Technological UniversityHoughtonUSA

Personalised recommendations