Designs, Codes and Cryptography

, Volume 57, Issue 3, pp 329–346 | Cite as

Self-dual codes with automorphism of order 3 having 8 cycles



All optimal binary self-dual codes which have an automorphism of order 3 with 8 independent cycles are obtained up to equivalence.


Automorphism of type p-(c, fHermitian code Optimal codes Self-dual codes Weight enumerators 

Mathematics Subject Classification (2000)

11T71 94B05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bouyuklieva S.: Some optimal self-orthogonal and self-dual codes. Discrete Math. 287, 1–10 (2004).MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bouyukliev I.: Q-extension, on-line available at:
  3. 3.
    Bouyuklieva S., Yankov N., Russeva R.: Classification of the binary self-dual [42, 21, 8] codes having an automorphism of order 3. Finite Field. Appl. 13, 605–615 (2007).MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Huffman W.C.: On the classification and enumeration of self-dual codes. Finite Field. Appl. 11, 451–490 (2005).MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Yorgov V.Y.: Binary self-dual codes with automorphism of an odd order. Problems Inform. Trans. 19, 260–270 (1983).Google Scholar
  6. 6.
    Harada M., Munemasa A.: Some restrictions on weight enumerators of singly even self-dual codes. IEEE Trans. Inform. Theory 52, 1266–1269 (2006).CrossRefMathSciNetGoogle Scholar
  7. 7.
    Buyuklieva S., Yorgov V.Y.: Singly-even self-dual codes of length 40. Designs Codes Crypt. 9, 131–141 (1996).MATHMathSciNetGoogle Scholar
  8. 8.
    Conway J.H., Sloane N.J.A.: A new upper bound on the minimal distance of self-dual codes. IEEE Trans. Inform. Theory 36, 1319–1333 (1991).CrossRefMathSciNetGoogle Scholar
  9. 9.
    Huffman W.C.: Automorphisms of codes with application to extremal doubly-even codes of length 48. IEEE Trans. Inform. Theory 28, 511–521 (1982).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pless V., Sloane N.J.A, Ward H.N.: Ternary codes of minimum weight 6 and the classification of the self-dual codes of length 20. IEEE Trans. Inform. Theory 26, 306–316 (1980).CrossRefMathSciNetGoogle Scholar
  11. 11.
    Conway J.H., Pless V., Sloane N.J.A.: Self-dual codes over GF(3) and GF(4) of length not exceeding 16. IEEE Trans. Inform. Theory 25, 321–322 (1979).CrossRefMathSciNetGoogle Scholar
  12. 12.
    Bouyukliev I., Bouyuklieva S., Gulliver T.A., Östergåard P.: Classification of optimal binary self-orthogonal codes. J. Comb. Math. Comb. Comput. 59, 33–87 (2006).MATHGoogle Scholar
  13. 13.
    Yorgov V.Y. (1987) A method for constructing inequivalent self-dual codes with applications to length 56. IEEE Trans. Inform. Theory 33, 77–82 .MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Jaffe D.B.: Information about binary linear codes, on-line available at

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsYonsei UniversitySeoulKorea

Personalised recommendations