论文标题
来自MDS Hermitian自动执行代码的新的MD纠缠辅助量子代码
New MDS Entanglement-Assisted Quantum Codes from MDS Hermitian Self-Orthogonal Codes
论文作者
论文摘要
线性代码$ {\ bf c} \ subset {\ bf c} \ subset {\ bf f} _ {q^2} $的交叉点 代码。线性代码$ {\ bf c} \ subset {\ bf f} _ {q^2} $满足$ {\ bf c} \ subset {\ bf c}^{\ bf c}^{\ perp_h} $被称为Hermitian selfortorthroconal。为MDS量子误差校正代码（QECC）构建了许多Hermitian自动守则。在本文中，我们证明，对于满足$ 0 \ leq h \ leq k $的非负整数$ h $，是线性的Hermitian hermitian subporonal $ [n，k] _ {q^2} $代码等同于线性$ h $ h $ dimension hermitian hermitian hermitian helmitian hull hull code。因此，许多新的MD纠缠量误差校正（EAQEC）代码可以从先前已知的Hermitian自动执行代码构建。实际上，我们的方法表明，可以将以前从Hermitian自动代码的构造量子MDS代码直接转换为具有非零消耗参数$ c $的MDS纠缠辅助量子代码。我们证明MDS EAQEC $ [[n，k，d，c]] _ q $ codes具有非零$ c $参数，而$ d \ leq \ frac {n+2} {2} {2} {2} {2} $对于任意长度$ n \ leq q^2+1 $。此外，从$ k $二维的Hermitian自动执行代码构建的任何QECC都可以转换为$ K $不同的EAQEC代码。
The intersection ${\bf C}\bigcap {\bf C}^{\perp_H}$ of a linear code ${\bf C} \subset {\bf F}_{q^2}$ and its Hermitian dual ${\bf C}^{\perp_H}$ is called the Hermitian hull of this code. A linear code ${\bf C} \subset {\bf F}_{q^2}$ satisfying ${\bf C} \subset {\bf C}^{\perp_H}$ is called Hermitian self-orthogonal. Many Hermitian self-orthogonal codes were given for the construction of MDS quantum error correction codes (QECCs). In this paper we prove that for a nonnegative integer $h$ satisfying $0 \leq h \leq k$, a linear Hermitian self-orthogonal $[n, k]_{q^2}$ code is equivalent to a linear $h$-dimension Hermitian hull code. Therefore a lot of new MDS entanglement-assisted quantum error correction (EAQEC) codes can be constructed from previous known Hermitian self-orthogonal codes. Actually our method shows that previous constructed quantum MDS codes from Hermitian self-orthogonal codes can be transformed to MDS entanglement-assisted quantum codes with nonzero consumption parameter $c$ directly. We prove that MDS EAQEC $[[n, k, d, c]]_q$ codes with nonzero $c$ parameters and $d\leq \frac{n+2}{2}$ exist for arbitrary length $n \leq q^2+1$. Moreover any QECC constructed from $k$-dimensional Hermitian self-orthogonal codes can be transformed to $k$ different EAQEC codes.
