A method for constructing quaternary Hermitian self-dual codes and an application to quantum codes

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Abstract

We introduce quaternary modified four μ-circulant codes as a modification of four circulant codes. We give basic properties of quaternary modified four μ-circulant Hermitian self-dual codes. We also construct quaternary modified four μ-circulant Hermitian self-dual codes having large minimum weights. Two quaternary Hermitian self-dual [56, 28, 16] codes are constructed for the first time. These codes improve the previously known lower bound on the largest minimum weight among all quaternary (linear) [56, 28] codes. In addition, these codes imply the existence of a quantum [[56, 0, 16]] code.

Original languageEnglish
Pages (from-to)2927-2948
Number of pages22
JournalDesigns, Codes, and Cryptography
Volume92
Issue number10
DOIs
Publication statusPublished - 2024 Oct

Keywords

  • 94B05
  • Hermitian self-dual code
  • Quaternary code
  • Self-dual code

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