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

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 d...

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Bibliographic Details
Published in:arXiv.org 2016-10
Main Authors: Galindo, Carlos, Geil, Olav, Hernando, Fernando, Ruano, Diego
Format: Article
Language:English
Subjects:
Binary system
Codes
Parameters
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1610.07891