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arXiv · 1610.07891

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

Carlos Galindo·Olav Geil·Fernando Hernando·Diego Ruano
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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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Carlos Galindo, Olav Geil, Fernando Hernando, Diego Ruano. 2016-10-25. On the distance of stabilizer quantum codes from $J$-affine variety codes. https://doi.org/10.1007/s11128-017-1559-1

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