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Error-Correcting Codes over an Alphabet of Four Elements

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Abstract

The problem of finding the values of Aq(n,d)—the maximum size of a code of length n and minimum distance d over an alphabet of q elements—is considered. Upper and lower bounds on A4(n,d) are presented and some values of this function are settled. A table of best known bounds on A4(n,d) is given for n ≤ 12. When q ≤ M < 2q, all parameters for which Aq(n,d) = M are determined.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, P.O. Box 323, 5000, V. Tarnovo, Bulgaria

    Galina T. Bogdanova

  2. Department of Mathematics, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Andries E. Brouwer

  3. Department of Mathematics, Technical University, 5300, Gabrovo, Bulgaria

    Stoian N. Kapralov

  4. Department of Computer Science and Engineering, Helsinki University of Technology, P.O. Box 5400, 02015 HUT, Finland

    Patric R. J. Östergård

Authors
  1. Galina T. Bogdanova
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  2. Andries E. Brouwer
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  3. Stoian N. Kapralov
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  4. Patric R. J. Östergård
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Bogdanova, G.T., Brouwer, A.E., Kapralov, S.N. et al. Error-Correcting Codes over an Alphabet of Four Elements. Designs, Codes and Cryptography 23, 333–342 (2001). https://doi.org/10.1023/A:1011275112159

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