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Quantum Information Processing

, Volume 14, Issue 9, pp 3211–3231 | Cite as

Stabilizer quantum codes from J-affine variety codes and a new Steane-like enlargement

  • Carlos Galindo
  • Fernando Hernando
  • Diego Ruano
Article

Abstract

New stabilizer codes with parameters better than the ones available in the literature are provided in this work, in particular quantum codes with parameters \([[127,63, {\ge }12]]_2\) and \([[63,45, {\ge }6]]_4\) that are records. These codes are constructed with a new generalization of the Steane’s enlargement procedure and by considering orthogonal subfield-subcodes—with respect to the Euclidean and Hermitian inner product—of a new family of linear codes, the J-affine variety codes.

Keywords

Stabilizer J-affine variety codes Subfield-subcodes  Steane enlargement Hermitian and Euclidean duality 

Notes

Acknowledgments

The authors wish to thank Ryutaroh Matsumoto and the anonymous reviewers for helpful comments on this paper.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Carlos Galindo
    • 1
  • Fernando Hernando
    • 1
  • Diego Ruano
    • 2
  1. 1.Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones de CastellónUniversitat Jaume ICastellón de la PlanaSpain
  2. 2.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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