Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912160363315200 |
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| author | Bag, Tushar Dinh, Hai Q Panario, Daniel |
| author_facet | Bag, Tushar Dinh, Hai Q Panario, Daniel |
| contents | This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both matrix and polynomial approaches. We provide two versions of necessary and sufficient conditions for two-generator quasi-cyclic codes for symplectic self-orthogonality and the symplectic dual-containing condition. Additionally, using these necessary and sufficient conditions, we construct new quantum codes with record-breaking parameters that improve upon current records. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes Bag, Tushar Dinh, Hai Q Panario, Daniel Information Theory This article studies one-generator and two-generator quasi-cyclic codes over finite fields. We present two versions of necessary and sufficient conditions for the symplectic selforthogonality of one-generator quasi-cyclic codes, using both matrix and polynomial approaches. We provide two versions of necessary and sufficient conditions for two-generator quasi-cyclic codes for symplectic self-orthogonality and the symplectic dual-containing condition. Additionally, using these necessary and sufficient conditions, we construct new quantum codes with record-breaking parameters that improve upon current records. |
| title | Some New Non-binary Quantum Codes from One-generator Quasi-cyclic Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2412.13613 |