On the minimum weights of binary LCD codes and ternary 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 codes trivially. We study the largest minimum weight d2(n,k) among all binary LCD [n,k] codes and the largest minimum weight d3(n,k) among all ternary LCD [n,k] codes. The largest minimum weights d2(n,5) and d3(n,4) are partially determined. We also determine the largest minimum weights d2(n,n−5), d3(n,n−i) for i∈{2,3,4}, and d3(n,k) for n∈{11,12,…,19}.

Original languageEnglish
Article number101925
JournalFinite Fields and their Applications
Volume76
DOIs
Publication statusPublished - 2021 Dec

Keywords

  • Binary code
  • Linear complementary dual code
  • Minimum weight
  • Ternary code

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Engineering(all)
  • Applied Mathematics

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