Construction of MDS self-dual codes over Galois rings

Jon Lark Kim, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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.

Original languageEnglish
Pages (from-to)247-258
Number of pages12
JournalDesigns, Codes, and Cryptography
Volume45
Issue number2
DOIs
StatePublished - Nov 2007

Keywords

  • Galois ring
  • MDS code
  • Self-dual code

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