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The Nonexistence of Ternary [50,5,32] Codes

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Abstract

It is unknown (cf. Hill and Newton [8] or Hamada [3]) whether or not there exists a ternary [50,5,32] code meeting the Griesmer bound. The purpose of this paper is to prove the nonexistence of ternary [50,5,32] codes. Since there exists a ternary [51,5,32] code, this implies that n3(5,32) = 51, where n3(k,d) denotes the smallest value of n for which there exists a ternary [n,k,d] code.

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Authors and Affiliations

  1. University of Technology, Den Dolech 2, 5600 MB, Eindhoven, The Netherlands

    Marijn Van Eupen

  2. Department of Applied Mathematics, Osaka Women's University, Daisen-cho, Sakai, Osaka 590, Japan

    Noboru Hamada & Yoko Watamori

Authors
  1. Marijn Van Eupen
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  2. Noboru Hamada
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  3. Yoko Watamori
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Van Eupen, M., Hamada, N. & Watamori, Y. The Nonexistence of Ternary [50,5,32] Codes. Designs, Codes and Cryptography 7, 235–237 (1996). https://doi.org/10.1023/A:1018042823954

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