On Quantum and Classical BCH Codes

Classical Bose-Chaudhuri-Hocquenghem (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...

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Veröffentlicht in:	IEEE transactions on information theory 2007-03, Vol.53 (3), p.1183-1188
Hauptverfasser:	Aly, S.A., Klappenecker, A., Sarvepalli, P.K.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Bose-Chaudhuri-Hocquenghem (BCH) codes Code standards Codes Coding, codes Computer science dimension dual codes Engineering profession Exact sciences and technology Galois fields Information processing Information theory Information, signal and communications theory minimum distance quantum codes Quantum mechanics Quantum theory Signal and communications theory Studies Sufficient conditions Telecommunications and information theory Upper bound
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Zusammenfassung:	Classical Bose-Chaudhuri-Hocquenghem (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 delta=O(radicn), 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
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2006.890730