Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.12519 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918249515450368 |
|---|---|
| author | Wang, Jiabin Luo, Jinquan |
| author_facet | Wang, Jiabin Luo, Jinquan |
| contents | In this paper, we study the enumerative and asymptotic properties related to Hermitian $\ell$-complementary codes on the unitary space over $\F_{q^2}$. We provide some closed form expressions for the counting formulas of Hermitian $\ell$-complementary codes. There is a similarity in the asymptotic weight distribution between Hermitian self-orthogonal codes and unrestricted codes. Furthermore, we study the asymptotic behavior of Hermitian self-orthogonal codes whose minimum distance is at least $d$. In particular, we conclude that MDS codes within the class of Hermitian self-orthogonal codes are asymptotically dense when the alphabet size approaches to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linear Codes with Certain Dimension of Hermitian Hulls Wang, Jiabin Luo, Jinquan Information Theory Rings and Algebras In this paper, we study the enumerative and asymptotic properties related to Hermitian $\ell$-complementary codes on the unitary space over $\F_{q^2}$. We provide some closed form expressions for the counting formulas of Hermitian $\ell$-complementary codes. There is a similarity in the asymptotic weight distribution between Hermitian self-orthogonal codes and unrestricted codes. Furthermore, we study the asymptotic behavior of Hermitian self-orthogonal codes whose minimum distance is at least $d$. In particular, we conclude that MDS codes within the class of Hermitian self-orthogonal codes are asymptotically dense when the alphabet size approaches to infinity. |
| title | Linear Codes with Certain Dimension of Hermitian Hulls |
| topic | Information Theory Rings and Algebras |
| url | https://arxiv.org/abs/2512.12519 |