On Quantum and Classical BCH Codes
Quantum Physics
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.quant-ph/0604102,
title = {On Quantum and Classical BCH Codes},
author = {Salah A. Aly and Andreas Klappenecker and Pradeep Kiran Sarvepalli},
journal= {arXiv preprint arXiv:quant-ph/0604102},
year = {2007}
}
Comments
17 pages, LaTeX