Application of constacyclic codes to quantum MDS codes
Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over Fq2 satisfying C ┴ H ⊆ C, where C ┴ H denotes the Hermitian dual code of C. For a linear code C of length n over Fq2 ,...
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sg-ntu-dr.10356-1072372023-02-28T19:39:55Z Application of constacyclic codes to quantum MDS codes Chen, Bocong Ling, San Zhang, Guanghui School of Physical and Mathematical Sciences DRNTU::Science::Chemistry::Physical chemistry::Quantum chemistry Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over Fq2 satisfying C ┴ H ⊆ C, where C ┴ H denotes the Hermitian dual code of C. For a linear code C of length n over Fq2 , we say that C is a dual-containing code if C ┴ H ⊆ C and C ̸= Fn q2 . Several classes of new quantum MDS codes with relatively large minimum distance have been produced through dual-containing constacyclic MDS codes (see [15], [17], [24], [25]). These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed. Consequently, quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have minimum distance bigger than the ones available in the literature. Accepted version 2015-04-22T03:13:40Z 2019-12-06T22:27:14Z 2015-04-22T03:13:40Z 2019-12-06T22:27:14Z 2015 2015 Journal Article Chen, B., Ling, S., & Zhang, G. (2015). Application of constacyclic codes to quantum MDS codes. IEEE transactions on information theory, 61(3), 1474-1484. https://hdl.handle.net/10356/107237 http://hdl.handle.net/10220/25434 10.1109/TIT.2015.2388576 185838 en IEEE transactions on information theory © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [Article DOI: http://dx.doi.org/10.1109/TIT.2015.2388576]. 11 p. application/pdf |
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DRNTU::Science::Chemistry::Physical chemistry::Quantum chemistry Chen, Bocong Ling, San Zhang, Guanghui Application of constacyclic codes to quantum MDS codes |
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Quantum maximum-distance-separable (MDS) codes form an important class of quantum codes. To get q-ary quantum MDS codes, one of the effective ways is to find linear MDS codes C over Fq2 satisfying C ┴ H ⊆ C, where C ┴ H denotes the Hermitian dual code of C. For a linear code C of length n over Fq2 , we say that C is a dual-containing code if C ┴ H ⊆ C and C ̸= Fn q2 . Several classes of new quantum MDS codes with relatively large minimum distance have been produced through dual-containing constacyclic MDS codes (see [15], [17], [24], [25]). These works motivate us to make a careful study on the existence conditions for dual-containing constacyclic codes. We obtain necessary and sufficient conditions for the existence of dual-containing constacyclic codes. Four classes of dual-containing constacyclic MDS codes are constructed and their parameters are computed. Consequently, quantum MDS codes are derived from these parameters. The quantum MDS codes exhibited here have minimum distance bigger than the ones available in the literature. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Chen, Bocong Ling, San Zhang, Guanghui |
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Article |
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Chen, Bocong Ling, San Zhang, Guanghui |
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Chen, Bocong |
title |
Application of constacyclic codes to quantum MDS codes |
title_short |
Application of constacyclic codes to quantum MDS codes |
title_full |
Application of constacyclic codes to quantum MDS codes |
title_fullStr |
Application of constacyclic codes to quantum MDS codes |
title_full_unstemmed |
Application of constacyclic codes to quantum MDS codes |
title_sort |
application of constacyclic codes to quantum mds codes |
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2015 |
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https://hdl.handle.net/10356/107237 http://hdl.handle.net/10220/25434 |
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