Skip to main content
Log in

On the Binary Self-Dual Codes with an Automorphism of Order 2

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Methods to design binary self-dual codes with an automorphism of order two without fixed points are presented. New extremal self-dual [40,20,8], [42,21,8],[44,22,8] and [64,32,12] codes with previously not known weight enumerators are constructed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. A. Brualdi and V. Pless, Weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, Vol. 37 (1991) pp. 1222–1225.

    Google Scholar 

  2. F. C. Bussemaker and V. D. Tonchev, Extremal doubly-even codes of length 40 derived from Hadamard matrices of order 20, Discrete Math., Vol. 82 (1990) pp. 317–321.

    Google Scholar 

  3. St. Buyuklieva, Existence of certain extremal self-dual codes of lengths 42 and 44: Proceedings of the International Workshop OCRT, Sozopol, Bulgaria (1995) pp. 29–31.

  4. St. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40, Designs, Codes and Cryptography (to appear).

  5. J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, Vol. 36 (1991) pp. 1319–1333.

    Google Scholar 

  6. T. A. Gulliver and M. Harada, Weight enumerators of double circulant codes and new extremal self-dual codes, preprint.

  7. M. Harada, T. A. Gulliver and H. Kaneta, Classification of extremal double circulant self-dual codes of length up to 62, preprint.

  8. M. Harada, Existence of new extremal double-even codes and extremal singly-even codes, Designs, Codes and Cryptography, Vol. 8 (1996) pp. 1–12.

    Google Scholar 

  9. M. Harada and H. Kimura, New extremal doubly-even [64, 32, 12] codes, Designs, Codes and Cryptography, Vol. 6 (1995) pp. 91–96.

    Google Scholar 

  10. M. Harada and V. D. Tonchev, Singly-even self-dual codes and Hadamard matrices, Lecture Notes in Computer Science, Vol. 948 (1995) pp. 279–284.

  11. W. C. Huffman, Automorphisms of codes with application to extremal doubly-even codes of length 48, IEEE Trans. Inform. Theory, Vol. 28 (1982) pp. 511–521.

    Google Scholar 

  12. S. Kapralov and V. Tonchev, Extremal doubly-even codes of length 64 derived from symmetric designs, Discrete Math., Vol. 83 (1990) pp. 285–289.

    Google Scholar 

  13. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, The Netherlands (1977).

    Google Scholar 

  14. G. Pasquier, A binary extremal doubly-even self-dual code [64, 32, 12] obtained from an extended Reed-Solomon code over F 16, IEEE Trans. Inform. Theory, Vol. 27 (1981) pp. 807–808.

    Google Scholar 

  15. V. Pless, V. Tonchev and J. Leon, On the existence of a certain [64, 32, 12] extremal code, IEEE Trans. Inform. Theory, Vol. 39 (1993) pp. 214–215.

    Google Scholar 

  16. R. Ruseva and V. Yorgov, Two exceptional extremal codes (in Russian), Probl. Pered. Inform., Vol. 29 (1993) pp. 99–103.

    Google Scholar 

  17. E. Spence and V. D. Tonchev, Extremal self-dual codes from symmetric designs, Discrete Math., Vol. 110 (1992) pp. 265–268.

    Google Scholar 

  18. V. D. Tonchev, Self-orthogonal designs and extremal doubly-even codes, J. Combin. Theory, Ser. A, Vol. 52 (1989) pp. 197–205.

    Google Scholar 

  19. H. P. Tsai, Existence of certain extremal self-dual codes, IEEE Trans. Inform. Theory, Vol. 38 (1992) pp. 501–504.

    Google Scholar 

  20. V. Y. Yorgov, Binary self-dual codes with automorphisms of odd order (in Russian), Probl. Pered. Inform., Vol. 19 (1983) pp. 11–24.

    Google Scholar 

  21. V. Y. Yorgov, A method for constructing inequivalent self-dual codes with applications to length 56, IEEE Trans. Inform. Theory, Vol. 33 (1987) pp. 77–82.

    Google Scholar 

  22. V. Y. Yorgov, Doubly-even extremal codes of length 64 (in Russian), Probl. Pered. Inform., Vol. 22 (1986) pp. 277–284.

    Google Scholar 

  23. V. Y. Yorgov, New extremal singly-even self-dual codes of length 44: Proceedings of the Sixth Joint Swedish-Russian International Workshop on Information Theory, Sweden (1993) pp. 372–375.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Buyuklieva, S. On the Binary Self-Dual Codes with an Automorphism of Order 2. Designs, Codes and Cryptography 12, 39–48 (1997). https://doi.org/10.1023/A:1008289725040

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008289725040

Navigation