Quaternary Hermitian Linear Complementary Dual Codes

Makoto Araya, Masaaki Harada, Ken Saito

Research output: Contribution to journalArticlepeer-review

Abstract

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension 2. In this paper, we give some conditions on the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As a consequence, we completely determine the largest minimum weights for dimension 3, by using a classification of some quaternary codes. In addition, for a positive integer s, an entanglement-assisted quantum error-correcting $[[21{s}+5,3,16{s}+3;21{s}+2]]$ code with maximal entanglement is constructed for the first time from a quaternary Hermitian linear complementary dual [26, 3, 19] code.

Original languageEnglish
Article number8887244
Pages (from-to)2751-2759
Number of pages9
JournalIEEE Transactions on Information Theory
Volume66
Issue number5
DOIs
Publication statusPublished - 2020 May

Keywords

  • Griesmer bound
  • Hermitian linear complementary dual code
  • Quaternary code

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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