Steane-Enlargement of Quantum Codes from the Hermitian Curve

Research output: Working paperResearch

Abstract

In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. 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.
Original languageEnglish
PublisherarXiv.org
Number of pages11
Publication statusPublished - 22 Apr 2019

Keywords

  • algebraic geometric codes
  • quantum code
  • Steane-enlargement
  • Hermitian curve

Cite this

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title = "Steane-Enlargement of Quantum Codes from the Hermitian Curve",
abstract = "In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. 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.",
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AB - In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. 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.

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