Constructions of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916160598966272 |
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| author | Zheng, Xiujing Wang, Liqi Zhu, Shixin |
| author_facet | Zheng, Xiujing Wang, Liqi Zhu, Shixin |
| contents | By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed-Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of ebits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of $q^2-1$, which are completely new and unlike all those known lengths existed before. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14505 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Constructions of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes Zheng, Xiujing Wang, Liqi Zhu, Shixin Information Theory 94B05, 81p70 E.4 By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three classes of entanglement-assisted quantum error-correcting maximum-distance-separable (EAQMDS) codes are constructed through generalized Reed-Solomon codes. Under our constructions, the minimum distances of our EAQMDS codes are much larger than those of the known EAQMDS codes of the same lengths that consume the same number of ebits. Furthermore, some of the lengths of the EAQMDS codes are not divisors of $q^2-1$, which are completely new and unlike all those known lengths existed before. |
| title | Constructions of entanglement-assisted quantum MDS codes from generalized Reed-Solomon codes |
| topic | Information Theory 94B05, 81p70 E.4 |
| url | https://arxiv.org/abs/2210.14505 |