Let \(R=\mathbb {F}_{q^{2}}+u \mathbb {F}_{q^{2}},\) where \(\mathbb {F}_{q^{2}}\) is the finite field with q² elements, q is a power of a prime p, and u² = 0. In this paper, a class of maximal entanglement entanglement-assisted quantum error-correcting codes (EAQECCs) is obtained by employing (1 − u)-constacyclic Hermitian linear complementary dual (LCD) codes of length n over R. First, we give a sufficient condition for a linear code C of length n over R to be a Hermitian LCD code and claim that there does not exist a non-free Hermitian LCD code of length n over R. Also, assume that \(\gcd (n, q)=1\), and γ is a unit in R, we obtain all γ-constacyclic Hermitian LCD codes. Finally, we derive symplectic LCD codes of length 2n over \(\mathbb {F}_{q^{2}}\) as Gray images of linear and constacyclic codes of length n over R. By using the explicit symplectic method in Galindo et al. (Quantum Inf. Process. 18(4), 116 9), we get the desired maximal entanglement EAQECCs.

让\(R=\mathbb {F}_{q^{2}}+u \mathbb {F}_{q^{2}},\)其中\(\mathbb {F}_{q^{2 }}\)是具有q ^{2 个}元素的有限域，q是素数p的幂，u ² = 0。 本文得到一类最大纠缠纠缠辅助量子纠错码(EAQECCs)通过在R上使用长度为n 的(1 − u )-constacyclic Hermitian 线性互补对偶 (LCD) 码。首先，我们给出一个长度为n的线性代码C在R 上的充分条件成为 Hermitian LCD 代码并声称不存在长度为n超过R的非自由 Hermitian LCD 代码。此外，假设\(\gcd (n, q)=1\)，并且γ是R 中的一个单位，我们获得所有γ -constacyclic Hermitian LCD 代码。最后，我们得出长度为2的辛LCD码Ñ超过\（\ mathbb {F} _ {Q ^ {2}} \）作为线性的灰色图像和长度的常循环码Ñ超过ř。通过使用 Galindo 等人的显式辛方法。（Quantum Inf. Process. 18 (4), 116 9），我们得到了所需的最大纠缠 EAQECC。