Construction of Some New Quantum BCH Codes

Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. One can construct quantum stabilizer codes with good parameters using classical BCH codes. In this paper, our goal is to find such classical BCH codes. We study some properties of suitable cyclotomic c...

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Bibliographic Details
Published in:IEEE access 2018-01, Vol.6, p.36122-36131
Main Authors: Zhang, Ming, Li, Zhuo, Xing, Lijuan, Tang, Nianqi
Format: Article
Language:English
Subjects:
BCH codes
Bose-Chaudhuri-Hocquenghem codes
Cascading style sheets
cyclotomic cosets
Enlargement
Error correction codes
Fields (mathematics)
Intserv networks
Linear codes
Lower bounds
Parameters
Quantum computing
Quantum mechanics
stabilizer codes
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Summary:Classical Bose-Chaudhuri-Hocquenghem (BCH) codes over finite fields have been studied extensively. One can construct quantum stabilizer codes with good parameters using classical BCH codes. In this paper, our goal is to find such classical BCH codes. We study some properties of suitable cyclotomic cosets at first. These results make it possible to construct nonbinary quantum BCH codes with a given parameter set. Several new families of quantum BCH codes obtained are based on Steane's enlargement of nonbinary Calderbank-Shor-Steane codes and Hermitian construction, respectively. Meanwhile, we have shown that the cyclotomic cosets given in our schemes are optimal to design quantum BCH codes. The defining set contains most consecutive integers. Therefore, corresponding quantum stabilizer codes have better lower bound of minimum distance. Furthermore, it is convenient to compute the dimension of new quantum codes. Compared with the ones available in the literature, the quantum BCH codes in our schemes have good parameters. In particular, we extend known results to more general case.
ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2018.2851075