Hulls of projective Reed-Muller codes over the projective plane
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917939729399808 |
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| author | Ruano, Diego San-José, Rodrigo |
| author_facet | Ruano, Diego San-José, Rodrigo |
| contents | By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of maximally entangled pairs required for the corresponding entanglement-assisted quantum error-correcting code. Hence, by computing the dimension of the hull we now have all the parameters of the symmetric and asymmetric entanglement-assisted quantum error-correcting codes constructed with projective Reed-Muller codes over the projective plane. As a byproduct, we also compute the dimension of the Hermitian hull for affine Reed-Muller codes in 2 variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13921 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hulls of projective Reed-Muller codes over the projective plane Ruano, Diego San-José, Rodrigo Information Theory Commutative Algebra 81P70 (Primary) 94B05, 13P25 (Secondary) By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of maximally entangled pairs required for the corresponding entanglement-assisted quantum error-correcting code. Hence, by computing the dimension of the hull we now have all the parameters of the symmetric and asymmetric entanglement-assisted quantum error-correcting codes constructed with projective Reed-Muller codes over the projective plane. As a byproduct, we also compute the dimension of the Hermitian hull for affine Reed-Muller codes in 2 variables. |
| title | Hulls of projective Reed-Muller codes over the projective plane |
| topic | Information Theory Commutative Algebra 81P70 (Primary) 94B05, 13P25 (Secondary) |
| url | https://arxiv.org/abs/2312.13921 |