Construction of MDS self-dual codes over Galois rings

  • Authors:
  • Jon-Lark Kim;Yoonjin Lee

  • Affiliations:
  • Department of Mathematics, University of Louisville, Louisville, USA 40292;Department of Mathematics, Ewha W. University, Seoul, South Korea

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2007

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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.