On Arbitrary Dimension Hermitian Hull linear codes from Hermitian self-orthogonal codes and New Hermitian Self-Orthogonal GRS Codes

Due to the important role of hulls of linear codes in coding theory, the problem about constructing arbitrary dimension hull linear codes has become a hot issue. In this paper, we generalize conclusions in \cite[]{RefJ47} and \cite[]{RefJ48} and prove that the Hermitian self-orthogonal codes of length $n$ can construct linear codes of length $n+2i$ and $n+2i+1$ with arbitrary-dimensional Hermitian hulls, where $i\geq 0$ is an integer. Then four new classes of Hermitian self-orthogonal GRS or extend GRS codes are constructed via two known multiplicative coset decompositions of $F_{q^2}$. The codes we constructed can be used to obtain new arbitrary dimension Galois hull linear codes by Theorems 11 and 12 in \cite[]{RefJ27} and finally we get many new EAQECCs whose code lengths ca take $n+2i$ and $n+2i+1$.