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On the distance of stabilizer quantum codes from J-affine variety codes

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Abstract

Self-orthogonal J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from J-affine variety codes and their subfield-subcodes. Moreover, this allows us to obtain new quantum codes, some of them either with better parameters, or with larger distances than the previously known codes.

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Authors and Affiliations

  1. Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I, Campus de Riu Sec., 12071, Castelló, Spain

    Carlos Galindo & Fernando Hernando

  2. Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220, Aalborg East, Denmark

    Olav Geil & Diego Ruano

Authors
  1. Carlos Galindo
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  2. Olav Geil
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  3. Fernando Hernando
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  4. Diego Ruano
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Corresponding author

Correspondence to Fernando Hernando.

Additional information

Supported by the Spanish Ministry of Economy/FEDER: Grants MTM2012-36917-C03-03 and MTM2015-65764-C3-2-P, the University Jaume I: Grant PB1-1B2015-02, and the Danish Council for Independent Research: Grant DFF-4002-00367.

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Galindo, C., Geil, O., Hernando, F. et al. On the distance of stabilizer quantum codes from J-affine variety codes. Quantum Inf Process 16, 111 (2017). https://doi.org/10.1007/s11128-017-1559-1

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