Abstract
All optimal binary self-dual codes which have an automorphism of order 3 with 8 independent cycles are obtained up to equivalence.
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Bouyuklieva S.: Some optimal self-orthogonal and self-dual codes. Discrete Math. 287, 1–10 (2004).
Bouyukliev I.: Q-extension, on-line available at: http://www.moi.math.bas.bg/~iliya/Q_ext.htm.
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).
Huffman W.C.: On the classification and enumeration of self-dual codes. Finite Field. Appl. 11, 451–490 (2005).
Yorgov V.Y.: Binary self-dual codes with automorphism of an odd order. Problems Inform. Trans. 19, 260–270 (1983).
Harada M., Munemasa A.: Some restrictions on weight enumerators of singly even self-dual codes. IEEE Trans. Inform. Theory 52, 1266–1269 (2006).
Buyuklieva S., Yorgov V.Y.: Singly-even self-dual codes of length 40. Designs Codes Crypt. 9, 131–141 (1996).
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).
Huffman W.C.: Automorphisms of codes with application to extremal doubly-even codes of length 48. IEEE Trans. Inform. Theory 28, 511–521 (1982).
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).
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).
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).
Yorgov V.Y. (1987) A method for constructing inequivalent self-dual codes with applications to length 56. IEEE Trans. Inform. Theory 33, 77–82 .
Jaffe D.B.: Information about binary linear codes, on-line available at http://www.math.unl.edu/~djaffe2/codes/webcodes/codeform.html.
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Communicated by J.D. Key.
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Kim, H.J. Self-dual codes with automorphism of order 3 having 8 cycles. Des. Codes Cryptogr. 57, 329–346 (2010). https://doi.org/10.1007/s10623-010-9370-3
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DOI: https://doi.org/10.1007/s10623-010-9370-3