On quantum and classical BCH codes Academic Article

abstract

• 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 = O(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. 2007 IEEE.

authors

• Klappenecker, Andreas

published proceedings

• IEEE TRANSACTIONS ON INFORMATION THEORY

author list (cited authors)

• Aly, S. A., Klappenecker, A., & Sarvepalli, P. K.

citation count

• 213

publication date

• March 2007

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

keywords

• Bose-chaudhuri-hocquenghem (bch) Codes
• Dimension
• Dual Codes
• Minimum Distance
• Quantum Codes

Digital Object Identifier (DOI)

• 10.1109/TIT.2006.890730

start page

• 1183

end page

• 1188

volume

• 53

issue

• 3

URL

• http://dx.doi.org/10.1109/tit.2006.890730