On Quantum and Classical BCH Codes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2007Embargo end date: 01 Apr 2006Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Information Theory, volume 53, pages 1,183-1,188 (issn: 0018-9448,

Copyright policy )Funded by:NSF | Efficient Decoherence Con..., NSF | CAREER: Design of Efficie...

Authors: Salah A. Aly; Andreas Klappenecker; Pradeep Kiran Sarvepalli;

doi: 10.1109/tit.2006.890730 , 10.48550/arxiv.quant-ph/0604102

arXiv: quant-ph/0604102

On Quantum and Classical BCH Codes

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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.

17 pages, LaTeX

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Keywords

Quantum Physics, FOS: Physical sciences, Quantum Physics (quant-ph)

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