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.

翻译：本文研究了在有限域 $\F_{q^2}$ 上酉空间中厄米特 $\ell$-互补码的计数与渐近性质。我们给出了厄米特 $\ell$-互补码计数公式的若干闭式表达式。厄米特自正交码与无约束码在渐近重量分布上存在相似性。此外，我们研究了最小距离至少为 $d$ 的厄米特自正交码的渐近行为。特别地，我们得出结论：当字母表大小趋于无穷时，在厄米特自正交码类中的最大距离可分码是渐近稠密的。