Steane-enlargement of quantum codes from the Hermitian function field

René Bødker Christensen*, Olav Geil

*Corresponding author

Research output: Contribution to journalJournal articleResearchpeer-review

1 Citation (Scopus)

Abstract

In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian function field. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In particular, the paper contains two constructions of quantum codes whose parameters are described by explicit formulae, and we show that these codes compare favourably to existing, comparable constructions in the literature. Furthermore, a number of the new codes meet or even exceed the quantum Gilbert–Varshamov bound.
Original languageEnglish
JournalDesigns, Codes and Cryptography
Volume88
Issue number8
Pages (from-to)1639-1652
Number of pages14
ISSN0925-1022
DOIs
Publication statusPublished - 11 Feb 2020

Keywords

  • algebraic geometric codes
  • quantum code
  • Steane-enlargement
  • Hermitian function field

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