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.
Similar content being viewed by others
References
R. A. Brualdi and V. Pless, Weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, Vol. 37 (1991) pp. 1222–1225.
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.
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.
St. Buyuklieva and V. Yorgov, Singly-even self-dual codes of length 40, Designs, Codes and Cryptography (to appear).
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.
T. A. Gulliver and M. Harada, Weight enumerators of double circulant codes and new extremal self-dual codes, preprint.
M. Harada, T. A. Gulliver and H. Kaneta, Classification of extremal double circulant self-dual codes of length up to 62, preprint.
M. Harada, Existence of new extremal double-even codes and extremal singly-even codes, Designs, Codes and Cryptography, Vol. 8 (1996) pp. 1–12.
M. Harada and H. Kimura, New extremal doubly-even [64, 32, 12] codes, Designs, Codes and Cryptography, Vol. 6 (1995) pp. 91–96.
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.
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.
S. Kapralov and V. Tonchev, Extremal doubly-even codes of length 64 derived from symmetric designs, Discrete Math., Vol. 83 (1990) pp. 285–289.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, The Netherlands (1977).
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.
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.
R. Ruseva and V. Yorgov, Two exceptional extremal codes (in Russian), Probl. Pered. Inform., Vol. 29 (1993) pp. 99–103.
E. Spence and V. D. Tonchev, Extremal self-dual codes from symmetric designs, Discrete Math., Vol. 110 (1992) pp. 265–268.
V. D. Tonchev, Self-orthogonal designs and extremal doubly-even codes, J. Combin. Theory, Ser. A, Vol. 52 (1989) pp. 197–205.
H. P. Tsai, Existence of certain extremal self-dual codes, IEEE Trans. Inform. Theory, Vol. 38 (1992) pp. 501–504.
V. Y. Yorgov, Binary self-dual codes with automorphisms of odd order (in Russian), Probl. Pered. Inform., Vol. 19 (1983) pp. 11–24.
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.
V. Y. Yorgov, Doubly-even extremal codes of length 64 (in Russian), Probl. Pered. Inform., Vol. 22 (1986) pp. 277–284.
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.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1008289725040