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On the support designs of extremal binary doubly even self-dual codes

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An Erratum to this article was published on 18 July 2014

Abstract

Let \(D\) be the support design of the minimum weight of an extremal binary doubly even self-dual \([24m,12m,4m+4]\) code. In this note, we consider the case when \(D\) becomes a \(t\)-design with \(t \ge 6\).

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References

  1. Assmus Jr. E.F., Mattson Jr. H.F.: New 5-designs. J. Comb. Theory 6, 122–151 (1969).

    Google Scholar 

  2. Bannai E., Koike M., Shinohara M., Tagami M.: Spherical designs attached to extremal lattices and the modulo p property of Fourier coefficients of extremal modular forms. Mosc. Math. J. 6, 225–264 (2006).

    Google Scholar 

  3. Bosma W., Cannon J., Playoust C.: The Magma algebra system I: the user language. J. Symb. Comp. 24(3/4), 235–265 (1997).

    Google Scholar 

  4. Calderbank A.R., Delsarte P., Sloane N.J.A.: A strengthening of the Assmus–Mattson theorem. IEEE Trans. Inf. Theory 37, 1261–1268 (1991).

    Google Scholar 

  5. Cameron P.J., van Lint J.H.: Designs, Graphs, Codes and Their Links, London Mathematical Society Student Texts 22. Cambridge University Press, Cambridge (1991).

  6. Koch H.: On self-dual doubly-even extremal codes. Discret. Math. 83(2–3), 291–300 (1990).

    Google Scholar 

  7. Tonchev V.D.: A characterization of designs related to the Witt system \(S(5,8,24)\). Math. Z. 191, 225–230 (1986).

    Google Scholar 

  8. Tonchev V. D.: Combinatorial configurations designs, codes, graphs (Translated from the Bulgarian). In: Melter R. A. (ed.) Pitman Monographs and Surveys in Pure and Applied Mathematics, 40. Longman Scientific & Technical, Harlow, Wiley, New York, (1988).

  9. Weisstein E. W.: Stirling Number of the Second Kind’. From MathWorld-A Wolfram Web Resource. http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html+ (2008).

  10. Zhang S.: On the nonexistence of extremal self-dual codes. Discret. Appl. Math. 91, 277–286 (1999).

    Google Scholar 

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 22840003, 24740031.

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Authors and Affiliations

  1. Graduate School of Science, Chiba University, Chiba, 263-8522, Japan

    Naoyuki Horiguchi

  2. Faculty of Education, Art and Science, Yamagata University, Yamagata, 990-8560, Japan

    Tsuyoshi Miezaki

  3. Graduate School of Natural Science and Technology, Okayama University, Okayama, 700-8530, Japan

    Hiroyuki Nakasora

Authors
  1. Naoyuki Horiguchi
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  2. Tsuyoshi Miezaki
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  3. Hiroyuki Nakasora
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Correspondence to Tsuyoshi Miezaki.

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Communicated by V. D. Tonchev.

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Horiguchi, N., Miezaki, T. & Nakasora, H. On the support designs of extremal binary doubly even self-dual codes. Des. Codes Cryptogr. 72, 529–537 (2014). https://doi.org/10.1007/s10623-012-9782-3

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  • DOI: https://doi.org/10.1007/s10623-012-9782-3

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