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Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes

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Abstract

The optimal one-error-correcting codes of length 13 that are doubly shortened perfect codes are classified utilizing the results of [Östergård, P.R.J., Pottonen, O.: The perfect binary one-error-correcting codes of length 15: Part I—Classification. IEEE Trans. Inform. Theory 55, 4657–4660 (2009)]; there are 117821 such (13,512,3) codes. By applying a switching operation to those codes, two more (13,512,3) codes are obtained, which are then not doubly shortened perfect codes.

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Author notes

  1. Olli Pottonen

    Present address: Finnish Defence Forces Technical Research Centre, P.O. Box 10, 11311, Riihimäki, Finland

Authors and Affiliations

  1. Department of Communications and Networking, Helsinki University of Technology TKK, P.O. Box 3000, 02015, TKK, Finland

    Patric R. J. Östergård & Olli Pottonen

Authors
  1. Patric R. J. Östergård
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  2. Olli Pottonen
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Correspondence to Patric R. J. Östergård.

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Östergård, P.R.J., Pottonen, O. Two optimal one-error-correcting codes of length 13 that are not doubly shortened perfect codes. Des. Codes Cryptogr. 59, 281–285 (2011). https://doi.org/10.1007/s10623-010-9450-4

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  • DOI: https://doi.org/10.1007/s10623-010-9450-4

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