Characterization and classification of optimal LCD codes

Makoto Araya, Masaaki Harada, Ken Saito

Research output: Contribution to journalArticlepeer-review

Abstract

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over Fq having large minimum weights for q∈ { 2 , 3 }. Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 4) , (3 , 2) , (3 , 3) }. Moreover, for arbitrary n, we give a complete classification of optimal LCD [n, k] codes over Fq, where (q, k) ∈ { (2 , 3) , (2 , 4) , (3 , 2) , (3 , 3) }.

Original languageEnglish
JournalDesigns, Codes, and Cryptography
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Binary code
  • Griesmer bound
  • Linear complementary dual code
  • Simple code
  • Ternary code

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics

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