Quantum LDPC Codes Based on Cocyclic Block Matrices
Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hen...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/9/1309 |
| _version_ | 1797580206946385920 |
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| author | Yuan Li Ying Guo |
| author_facet | Yuan Li Ying Guo |
| author_sort | Yuan Li |
| collection | DOAJ |
| description | Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum codes have the virtue of a fast construction algorithm. The recursive relation of a block matrix is employed in the proposed approach, so that the generator matrix of quantum cocyclic codes with long length can be constructed easily. Furthermore, the obtained quantum codes have the low-density advantage of there being no 4-cycles in the Tanner graph. |
| first_indexed | 2024-03-10T22:47:50Z |
| format | Article |
| id | doaj.art-f534ddb2dde846cfa25e8161923592a2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T22:47:50Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f534ddb2dde846cfa25e8161923592a22023-11-19T10:35:49ZengMDPI AGEntropy1099-43002023-09-01259130910.3390/e25091309Quantum LDPC Codes Based on Cocyclic Block MatricesYuan Li0Ying Guo1School of Electronic Information Engineering, Shanghai Dianji University, Shanghai 200240, ChinaSchool of Computer Science and Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaMotivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum codes have the virtue of a fast construction algorithm. The recursive relation of a block matrix is employed in the proposed approach, so that the generator matrix of quantum cocyclic codes with long length can be constructed easily. Furthermore, the obtained quantum codes have the low-density advantage of there being no 4-cycles in the Tanner graph.https://www.mdpi.com/1099-4300/25/9/1309long-length quantum codescocyclic block matricesstabilizer codeslow-density parity check codes |
| spellingShingle | Yuan Li Ying Guo Quantum LDPC Codes Based on Cocyclic Block Matrices Entropy long-length quantum codes cocyclic block matrices stabilizer codes low-density parity check codes |
| title | Quantum LDPC Codes Based on Cocyclic Block Matrices |
| title_full | Quantum LDPC Codes Based on Cocyclic Block Matrices |
| title_fullStr | Quantum LDPC Codes Based on Cocyclic Block Matrices |
| title_full_unstemmed | Quantum LDPC Codes Based on Cocyclic Block Matrices |
| title_short | Quantum LDPC Codes Based on Cocyclic Block Matrices |
| title_sort | quantum ldpc codes based on cocyclic block matrices |
| topic | long-length quantum codes cocyclic block matrices stabilizer codes low-density parity check codes |
| url | https://www.mdpi.com/1099-4300/25/9/1309 |
| work_keys_str_mv | AT yuanli quantumldpccodesbasedoncocyclicblockmatrices AT yingguo quantumldpccodesbasedoncocyclicblockmatrices |