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Self-Dual Codes Related to the Rudvalis Group

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Abstract

In this note, we will show that there exist exactly three self-dual codes with the automorphism group isomorphic to the Rudvalis group up to equivalence. Furthermore we will give some descriptions of codewords which span these codes. Especially, we will describe some codewords by using a relation between the rank 3 graph of the Rudvalis group and the Hoffman–Singleton graph.

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Authors and Affiliations

  1. Department of Mathematics, Kumamoto University, Kumamoto, 860-8555, Japan

    Naoki Chigira

  2. Department of Mathematics and Informatics, Chiba University, Chiba, 263-8522, Japan

    Masaaki Kitazume

Authors
  1. Naoki Chigira
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  2. Masaaki Kitazume
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Corresponding author

Correspondence to Naoki Chigira.

Additional information

This work is supported by JSPS KAKENHI Grant numbers 16K05066, 24340002.

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Chigira, N., Kitazume, M. Self-Dual Codes Related to the Rudvalis Group. Graphs and Combinatorics 34, 769–775 (2018). https://doi.org/10.1007/s00373-018-1912-x

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  • DOI: https://doi.org/10.1007/s00373-018-1912-x

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