Explicit MDS Codes with Complementary Duals

Peter Beelen, Lingfei Jin

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In 1964, Massey introduced a class of codes with complementary duals which are called Linear Complimentary Dual (LCD for short) codes. He showed that LCD codes have applications in communication system, side-channel attack (SCA) and so on. LCD codes have been extensively studied in literature. On the other hand, MDS codes form an optimal family of classical codes which have wide applications in both theory and practice. The main purpose of this paper is to give an explicit construction of several classes of LCD MDS codes, using tools from algebraic function fields. We exemplify this construction and obtain several classes of explicit LCD MDS codes for the odd characteristic case.
Original languageEnglish
JournalIEEE Transactions on Information Theory
Issue number11
Pages (from-to)7188-7193
Number of pages9
Publication statusPublished - 2018


  • Generalized Reed-Solomon codes
  • MDS codes
  • Linear complementary dual
  • Algebraic geometry codes

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