On Quantum and Classical BCH Codes

Author

Aly, Salah A. ; Klappenecker, Andreas ; Sarvepalli, Pradeep Kiran

Author_Institution

Dept. of Comput. Sci., Texas A&M Univ., College Station, TX

Volume

53

Issue

3

fYear

2007

fDate

3/1/2007 12:00:00 AM

Firstpage

1183

Lastpage

1188

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 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

Keywords

BCH codes; dual codes; classical BCH codes; dual codes; narrow-sense code; quantum stabilizer code; Code standards; Computer science; Engineering profession; Galois fields; Information processing; Information theory; Quantum mechanics; Sufficient conditions; Upper bound; Bose–Chaudhuri–Hocquenghem (BCH) codes; dimension; dual codes; minimum distance; quantum codes;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.890730

Filename

4106108