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On the minimum distance graph of an extended Preparata code

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Abstract

The minimum distance graph of an extended Preparata code P(m) has vertices corresponding to codewords and edges corresponding to pairs of codewords that are distance 6 apart. The clique structure of this graph is investigated and it is established that the minimum distance graphs of two extended Preparata codes are isomorphic if and only if the codes are equivalent.

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Authors and Affiliations

  1. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    C. Fernández-Córdoba

  2. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    K. T. Phelps

Authors
  1. C. Fernández-Córdoba
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  2. K. T. Phelps
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Correspondence to C. Fernández-Córdoba.

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Communicated by Victor A. Zinoviev.

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Fernández-Córdoba, C., Phelps, K.T. On the minimum distance graph of an extended Preparata code. Des. Codes Cryptogr. 57, 161–168 (2010). https://doi.org/10.1007/s10623-009-9358-z

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  • DOI: https://doi.org/10.1007/s10623-009-9358-z

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