Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929734844153856 |
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| author | Ruano, Diego San-José, Rodrigo |
| author_facet | Ruano, Diego San-José, Rodrigo |
| contents | Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the CSS construction and the Hermitian construction, respectively. We provide entanglement-assisted quantum error-correcting codes from projective Reed-Muller codes with flexible amounts of entanglement by considering equivalent codes. Moreover, we also construct quantum codes from subfield subcodes of projective Reed-Muller codes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem Ruano, Diego San-José, Rodrigo Information Theory 81P70 (Primary) 94B05, 13P25 (Secondary) Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the CSS construction and the Hermitian construction, respectively. We provide entanglement-assisted quantum error-correcting codes from projective Reed-Muller codes with flexible amounts of entanglement by considering equivalent codes. Moreover, we also construct quantum codes from subfield subcodes of projective Reed-Muller codes. |
| title | Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem |
| topic | Information Theory 81P70 (Primary) 94B05, 13P25 (Secondary) |
| url | https://arxiv.org/abs/2312.15308 |