New LCD MDS Codes of Non-Reed-Solomon Type

Yansheng Wu, Jong Yoon Hyun, Yoonjin Lee

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Both linear complementary dual (LCD) codes and maximum distance separable (MDS) codes have good algebraic structures, and they have interesting practical applications such as communication systems, data storage, quantum codes, and so on. So far, most of LCD MDS codes have been constructed by employing generalized Reed-Solomon codes. In this paper we construct some classes of new Euclidean LCD MDS codes and Hermitian LCD MDS codes which are not monomially equivalent to Reed-Solomon codes, called LCD MDS codes of non-Reed-Solomon type. Our method is based on the constructions of Beelen et al. (2017) and Roth and Lempel (1989). To the best of our knowledge, this is the first paper on the construction of LCD MDS codes of non-Reed-Solomon type; any LCD MDS code of non-Reed-Solomon type constructed by our method is not monomially equivalent to any LCD code constructed by the method of Carlet et al. (2018).

Original languageEnglish
Article number9447685
Pages (from-to)5069-5078
Number of pages10
JournalIEEE Transactions on Information Theory
Volume67
Issue number8
DOIs
StatePublished - Aug 2021

Keywords

  • LCD codes
  • Linear complementary dual codes
  • MDS codes
  • Reed-Solomon codes
  • non-Reed-Solomon codes

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