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Title: Application of constacyclic codes to quantum MDS codes
Authors: Chen, Bocong
Ling, San
Zhang, Guanghui
Keywords: DRNTU::Science::Chemistry::Physical chemistry::Quantum chemistry
Issue Date: 2015
Source: Chen, B., Ling, S., & Zhang, G. (2015). Application of constacyclic codes to quantum MDS codes. IEEE transactions on information theory, 61(3), 1474-1484.
Series/Report no.: IEEE transactions on information theory
Abstract: 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.
DOI: 10.1109/TIT.2015.2388576
Rights: © 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:].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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