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Designs, Codes and Cryptography

, Volume 59, Issue 1–3, pp 281–285 | Cite as

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

  • Patric R. J. Östergård
  • Olli Pottonen
Article

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.

Keywords

Hamming code Perfect code Shortening 

Mathematics Subject Classification (2000)

94B25 94B60 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Communications and NetworkingHelsinki University of Technology TKKTKKFinland
  2. 2.Finnish Defence Forces Technical Research CentreRiihimäkiFinland

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