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An optimal odd unimodular lattice in dimension 72

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Abstract

It is shown that if there is an extremal even unimodular lattice in dimension 72, then there is an optimal odd unimodular lattice in that dimension. Hence, the first example of an optimal odd unimodular lattice in dimension 72 is constructed from the extremal even unimodular lattice which has been recently found by G. Nebe.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Yamagata University, Yamagata, 990–8560, Japan

    Masaaki Harada

  2. PRESTO, Japan Science and Technology Agency (JST), Kawaguchi, Saitama, 332–0012, Japan

    Masaaki Harada

  3. Department of Mathematics, Oita National College of Technology, 1666 Oaza-Maki, Oita, 870–0152, Japan

    Tsuyoshi Miezaki

Authors
  1. Masaaki Harada
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  2. Tsuyoshi Miezaki
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Correspondence to Tsuyoshi Miezaki.

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This work was supported by JST PRESTO program.

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Harada, M., Miezaki, T. An optimal odd unimodular lattice in dimension 72. Arch. Math. 97, 529–533 (2011). https://doi.org/10.1007/s00013-011-0333-3

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  • DOI: https://doi.org/10.1007/s00013-011-0333-3

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