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Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2

Journal of Algebraic Combinatorics volume 57, pages 905–913 (2023)Cite this article

Abstract

In this note, we report the classification of all symmetric 2-(36, 15, 6) designs that admit an automorphism of order 2 and their incidence matrices generate an extremal ternary self-dual code. It is shown that up to isomorphism, there exists only one such design, having a full automorphism group of order 24, and the ternary code spanned by its incidence matrix is equivalent to the Pless symmetry code.

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Acknowledgements

The authors would like to thank the reviewers for their careful reading of the manuscript and for their constructive suggestions that led to an improvement of the exposition.

Funding

The first author is supported by Croatian Science Foundation under the project 6732.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Rijeka, 51000, Rijeka, Croatia

    Sanja Rukavina

  2. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Vladimir D. Tonchev

Authors
  1. Sanja Rukavina
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  2. Vladimir D. Tonchev
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Contributions

This is a joint collaboration with both authors contributing substantially throughout.

Corresponding author

Correspondence to Sanja Rukavina.

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Appendix

Appendix

figure a

A symmetric 2-(36, 15, 6) design associated with the Paley–Hadamard matrix of type II

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Rukavina, S., Tonchev, V.D. Extremal ternary self-dual codes of length 36 and symmetric 2-(36, 15, 6) designs with an automorphism of order 2. J Algebr Comb 57, 905–913 (2023). https://doi.org/10.1007/s10801-022-01206-2

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  • DOI: https://doi.org/10.1007/s10801-022-01206-2

Keywords

  • Pless symmetry code
  • Hadamard matrix
  • Symmetric 2-design
  • Automorphism group

Mathematics Subject Classification

  • 05B05
  • 05B20
  • 94B05

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