Construction of self-dual codes over finite rings Zpm

Heisook Lee, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

We present an efficient method for constructing self-dual or self-orthogonal codes over finite rings Zpm (or Zm) with p an odd prime and m a positive integer. This is an extension of the previous work [J.-L. Kim, Y. Lee, Euclidean and Hermitian self-dual MDS codes over large finite fields, J. Combin. Theory Ser. A 105 (2004) 79-95] over large finite fields GF (pm) to finite rings Zpm (or Zm). Using this method we construct self-dual or self-orthogonal codes of length at least up to 10 over various finite rings Zpm or Zp q with q an odd prime, where pm = 25, 125, 169, 289 and p q = 65, 85. All the self-dual codes we obtained are MDS, MDR, near MDS, or near MDR codes.

Original languageEnglish
Pages (from-to)407-422
Number of pages16
JournalJournal of Combinatorial Theory. Series A
Volume115
Issue number3
DOIs
StatePublished - Apr 2008

Keywords

  • Finite ring
  • MDR codes
  • MDS codes
  • Near MDR codes
  • Near MDS
  • Self-dual codes
  • Self-orthogonal codes

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