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Construction of MDS self-dual codes over Galois rings

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Abstract

The purpose of this paper is to construct nontrivial MDS self-dual codes over Galois rings. We consider a building-up construction of self-dual codes over Galois rings as a GF(q)-analogue of (Kim and Lee, J Combin Theory ser A, 105:79–95). We give a necessary and sufficient condition on which the building-up construction holds. We construct MDS self-dual codes of lengths up to 8 over GR(32,2), GR(33,2) and GR(34,2), and near-MDS self-dual codes of length 10 over these rings. In a similar manner, over GR(52,2), GR(53,2) and GR(72,2), we construct MDS self-dual codes of lengths up to 10 and near-MDS self-dual codes of length 12. Furthermore, over GR(112,2) we have MDS self-dual codes of lengths up to 12.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA

    Jon-Lark Kim

  2. Department of Mathematics, Ewha W. University, 120–750, Seoul, South Korea

    Yoonjin Lee

Authors
  1. Jon-Lark Kim
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  2. Yoonjin Lee
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Correspondence to Jon-Lark Kim.

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Communicated by: J.D. Key.

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Kim, JL., Lee, Y. Construction of MDS self-dual codes over Galois rings. Des. Codes Cryptogr. 45, 247–258 (2007). https://doi.org/10.1007/s10623-007-9117-y

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  • DOI: https://doi.org/10.1007/s10623-007-9117-y

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