Linear Codes with Certain Dimension of Hermitian Hulls
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866918249515450368 |
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| 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 |