Abstract
There are many analogies between codes, lattices, and vertex operator algebras. For example, extremal objects are good examples of combinatorial, spherical, and conformal designs. In this study, we investigated these objects from the aspect of design theory.
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Notes
Prof. Shimakura pointed us to the following: It can be proved that the homogeneous spaces of \(V_{\sqrt{2}{\mathbb {Z}}^{2}}\) are conformal 3-designs and not conformal 4-designs. Moreover, the homogeneous spaces of \(V_{A_{2}}\) are not conformal 6-designs [29].
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Acknowledgements
The author would like to thank Prof. Hiroki Shimakura, for his helpful discussions and contributions to this research. The author would also like to thank the anonymous reviewers for their beneficial comments on an earlier version of the manuscript. This work was supported by JSPS KAKENHI (18K03217).
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Communicated by L. Teirlinck.
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Miezaki, T. Design-theoretic analogies between codes, lattices, and vertex operator algebras. Des. Codes Cryptogr. 89, 763–780 (2021). https://doi.org/10.1007/s10623-021-00842-2
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DOI: https://doi.org/10.1007/s10623-021-00842-2