Linear Codes with Certain Dimension of Hermitian Hulls

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.

There is some overlap in content with existing papers. See "A further study on the mass formula for linear codes with prescribed hull dimension"