Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918528852951040 |
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| author | Ishizuka, Keita |
| author_facet | Ishizuka, Keita |
| contents | Extending recent work on the Euclidean hull, we derive closed-form ratio decompositions for the number of linear codes with prescribed Hermitian and symplectic hull dimension. The Hermitian ratio admits a uniform lower bound of at least $2/3$, while the symplectic ratio decays to $1/q^2$ asymptotically; a comparative analysis traces this qualitative difference to the Witt classification of the corresponding classical groups. The results translate directly into monotonicity statements for the number of entanglement-assisted quantum codes obtainable from Hermitian-hull-graded $[n, k]_{q^2}$ and symplectic-hull-graded $[2n, k]_q$ classical codes via the Guenda-Jitman-Gulliver and Wilde-Brun constructions, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29204 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions Ishizuka, Keita Combinatorics Extending recent work on the Euclidean hull, we derive closed-form ratio decompositions for the number of linear codes with prescribed Hermitian and symplectic hull dimension. The Hermitian ratio admits a uniform lower bound of at least $2/3$, while the symplectic ratio decays to $1/q^2$ asymptotically; a comparative analysis traces this qualitative difference to the Witt classification of the corresponding classical groups. The results translate directly into monotonicity statements for the number of entanglement-assisted quantum codes obtainable from Hermitian-hull-graded $[n, k]_{q^2}$ and symplectic-hull-graded $[2n, k]_q$ classical codes via the Guenda-Jitman-Gulliver and Wilde-Brun constructions, respectively. |
| title | Comparative monotonicity of linear codes by Hermitian and symplectic hull dimensions |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.29204 |