Hermitian hull of some GRS codes and new EAQMDS codes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909703672430592 |
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| author | Campion, Oisin San-José, Rodrigo |
| author_facet | Campion, Oisin San-José, Rodrigo |
| contents | We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a lattice. By solving this problem, we provide explicit formulas for the dimension of the hull, which determines the minimum number required of maximally entangled pairs for the associated entanglement-assisted quantum error-correcting codes. This flexible construction allows to obtain a wide range of entanglement-assisted quantum MDS codes, as well as new parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hermitian hull of some GRS codes and new EAQMDS codes Campion, Oisin San-José, Rodrigo Information Theory 81P70 (Primary) 94B05 (Secondary) We study the Hermitian hull of a particular family of generalized Reed-Solomon codes. The problem of computing the dimension of the hull is translated to a counting problem in a lattice. By solving this problem, we provide explicit formulas for the dimension of the hull, which determines the minimum number required of maximally entangled pairs for the associated entanglement-assisted quantum error-correcting codes. This flexible construction allows to obtain a wide range of entanglement-assisted quantum MDS codes, as well as new parameters. |
| title | Hermitian hull of some GRS codes and new EAQMDS codes |
| topic | Information Theory 81P70 (Primary) 94B05 (Secondary) |
| url | https://arxiv.org/abs/2507.18361 |