期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 53, 期 3, 页码 1183-1188出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2006.890730
关键词
Bose-Chaudhuri-Hocquenghem (BCH) codes; dimension; dual codes; minimum distance; quantum codes
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(root 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.
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