New Constructions of Quantum Stabilizer Codes Based on Difference Sets
In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/10/11/655 |
| _version_ | 1811184888053760000 |
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| author | Duc Manh Nguyen Sunghwan Kim |
| author_facet | Duc Manh Nguyen Sunghwan Kim |
| author_sort | Duc Manh Nguyen |
| collection | DOAJ |
| description | In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design. |
| first_indexed | 2024-04-11T13:21:04Z |
| format | Article |
| id | doaj.art-2349b2bc7f4a46e491dc680c13e250ab |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:21:04Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2349b2bc7f4a46e491dc680c13e250ab2022-12-22T04:22:12ZengMDPI AGSymmetry2073-89942018-11-01101165510.3390/sym10110655sym10110655New Constructions of Quantum Stabilizer Codes Based on Difference SetsDuc Manh Nguyen0Sunghwan Kim1School of Electrical Engineering, University of Ulsan, Ulsan 44610, KoreaSchool of Electrical Engineering, University of Ulsan, Ulsan 44610, KoreaIn this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-check matrices is first explained. Then, the proposed code construction is composed of three steps, which are to choose the generators of quantum stabilizer code, to determine the quantum stabilizer groups, and to determine subspace codewords with large minimum distance. The quantum stabilizer codes with various length are also presented to explain the practicality of the code construction. The proposed design can be applied to quantum stabilizer code construction based on combinatorial design.https://www.mdpi.com/2073-8994/10/11/655quantum informationquantum error correction codesquantum stabilizer codesdifference setssymplectic inner-product |
| spellingShingle | Duc Manh Nguyen Sunghwan Kim New Constructions of Quantum Stabilizer Codes Based on Difference Sets Symmetry quantum information quantum error correction codes quantum stabilizer codes difference sets symplectic inner-product |
| title | New Constructions of Quantum Stabilizer Codes Based on Difference Sets |
| title_full | New Constructions of Quantum Stabilizer Codes Based on Difference Sets |
| title_fullStr | New Constructions of Quantum Stabilizer Codes Based on Difference Sets |
| title_full_unstemmed | New Constructions of Quantum Stabilizer Codes Based on Difference Sets |
| title_short | New Constructions of Quantum Stabilizer Codes Based on Difference Sets |
| title_sort | new constructions of quantum stabilizer codes based on difference sets |
| topic | quantum information quantum error correction codes quantum stabilizer codes difference sets symplectic inner-product |
| url | https://www.mdpi.com/2073-8994/10/11/655 |
| work_keys_str_mv | AT ducmanhnguyen newconstructionsofquantumstabilizercodesbasedondifferencesets AT sunghwankim newconstructionsofquantumstabilizercodesbasedondifferencesets |