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New optimal [52, 26, 10] self-dual codes

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Abstract

We classify up to equivalence all optimal binary self-dual [52, 26, 10] codes having an automorphism of order 3 with 10 fixed points. We achieve this using a method for constructing self-dual codes via an automorphism of odd prime order. We study also codes with an automorphism of order 3 with 4 fixed points. Some of the constructed codes have new values β = 8, 9, and 12 for the parameter in their weight enumerator.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Shumen University, 9700, Shumen, Bulgaria

    Nikolay Yankov

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  1. Nikolay Yankov
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Correspondence to Nikolay Yankov.

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Communicated by J. D. Key.

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Yankov, N. New optimal [52, 26, 10] self-dual codes. Des. Codes Cryptogr. 69, 151–159 (2013). https://doi.org/10.1007/s10623-012-9639-9

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  • DOI: https://doi.org/10.1007/s10623-012-9639-9

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