On Quantum and Classical BCH Codes Academic Article uri icon

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 δ = 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.

author list (cited authors)

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

citation count

  • 182

publication date

  • March 2007