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On Quantum and Classical BCH Codes

Salah A. Aly·Andreas Klappenecker·Pradeep Kiran Sarvepalli
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Abstract

Classical BCH codes that contain their (Euclidean or Hermitian) dual codes can be used to construct quantum stabilizer codes; this correspondence studies the properties of such codes. It is shown that a BCH code of length n can contain its dual code only if its designed distance d=O(sqrt(n)), and the converse is proved in the case of narrow-sense codes. Furthermore, the dimension of narrow-sense BCH codes with small design distance is completely determined, and - consequently - the bounds on their minimum distance are improved. These results make it possible to determine the parameters of quantum BCH codes in terms of their design parameters.

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Salah A. Aly, Andreas Klappenecker, Pradeep Kiran Sarvepalli. 2006-04-14. On Quantum and Classical BCH Codes. https://arxiv.org/abs/quant-ph/0604102

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