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 = 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.

published proceedings

  • IEEE Transactions on Information Theory

author list (cited authors)

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

citation count

  • 205

complete list of authors

  • Aly, Salah A||Klappenecker, Andreas||Sarvepalli, Pradeep Kiran

publication date

  • March 2007