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arXiv · 2512.12519

Linear Codes with Certain Dimension of Hermitian Hulls

Jiabin Wang·Jinquan Luo
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Abstract

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.

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Jiabin Wang, Jinquan Luo. 2025-12-16. Linear Codes with Certain Dimension of Hermitian Hulls. https://arxiv.org/abs/2512.12519

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