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Quantum codes from affine variety codes and their subfield-subcodes

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Abstract

We use affine variety codes and their subfield-subcodes to obtain quantum stabilizer codes via the CSS code construction. With this procedure we get codes with good parameters, some of them exceeding the CSS quantum Gilbert–Varshamov bound given by Feng and Ma.

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Acknowledgments

This study was supported by Spain Ministry of Economy MTM2012-36917-C03-03 and University Jaume I: PB1-1B2012-04. The authors would like to thank three anonymous reviewers for their helpful comments.

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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

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  1. Carlos Galindo
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  2. Fernando Hernando
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Correspondence to Fernando Hernando.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Computer Algebra in Coding Theory and Cryptography”.

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Galindo, C., Hernando, F. Quantum codes from affine variety codes and their subfield-subcodes. Des. Codes Cryptogr. 76, 89–100 (2015). https://doi.org/10.1007/s10623-014-0016-8

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