Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.29204 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of 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.