We prove that any Hermitian self-orthogonal $[n,k,d]_{q^2}$ code gives rise to an $[n,k,d]_{q^2}$ code with $\ell$ dimensional Hermitian hull for $0\le \ell \le k$. We present a new method to construct Hermitian self-orthogonal $[n,k]_{q^2}$ codes with large dimensions $k>\frac{n+q-1}{q+1}$. New families of Hermitian self-orthogonal codes with good parameters are obtained; more precisely those containing almost MDS codes. By applying a puncturing technique to Hermitian self-orthogonal codes, MDS $[n,k]_{q^2}$ linear codes with Hermitian hull having large dimensions $k>\frac{n+q-1}{q+1}$ are also derived. New families of MDS, almost MDS and optimal codes with arbitrary Hermitian hull dimensions are explicitly constructed from algebraic curves. As an application, we provide entanglement-assisted quantum error correcting codes with new parameters.
翻译：我们证明,任何埃米提亚人自我或正反调的代码都会产生 $0\le\ ell\ el\ le k$. 我们提出了一个新方法来构建埃米提亚人自我或正反调的 $k,k)\ q ⁇ 2}$(美元) 大维的 $k ⁇ frac{n+q-1q+Q+1}$。 获得了具有良好参数的赫米提亚人自我或正反调代码的新家族; 更准确地说, 含有几乎 MDS 代码的新家族。 通过对赫米提亚人自我或正反调代码应用闪烁技术, MDS $n, k]\ q%2} 线性代码与赫米提亚人大维度的 $k ⁇ frac{n+q-1q+Q+1} 美元。 我们用新标准来修正海离子曲线。
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