The construction of maximum distance separable (MDS) linear complementary dual (LCD) codes and entanglement-assisted quantum MDS (EAQMDS) codes have been of a great interest. In this paper, for arbitrary prime power q , we construct two new families of MDS Hermitian LCD codes of length n = q 2 + 1 λ $n=\frac {{{q^{2}}+1}}{\lambda }$ and n = q 2 − 1 r , $n=\frac {q^{2}-1}{r},$ where r q + 1. By applying the obtained MDS Hermitian LCD codes to the EAQMDS codes, we derive new maximal entanglement EAQMDS codes of parameters q 2 + 1 λ , q 2 + 1 λ − l + 1 , l ; l − 1 q ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}}+1}}{\lambda },\frac {{{q^{2}}+1}}{\lambda }-l+1,l;l-1}\right ] \kern -0.30em\right ]_{q}}$ where 2 ≤ l ≤ q 2 + 1 + 2 λ 2 λ $2\leq l\leq \left \lfloor \frac {{{q^{2}}+1+2\lambda }}{2\lambda }\right \rfloor $ and q 2 − 1 r , q 2 − 1 r − γ , γ + 1 ; γ q ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}-}1}}{r},\frac {{{q^{2}-}1}}{r} -\gamma ,\gamma +1;\gamma }\right ] \kern -0.30em\right ]_{q}}$ where 1 ≤ γ ≤ q 2 − 1 2 r . $1\leq \gamma \leq \frac {{{q^{2}}-1}}{2r}.$

中文翻译：

---

具有最大纠缠的新纠缠辅助量子 MDS 码

最大距离可分 (MDS) 线性互补双 (LCD) 码和纠缠辅助量子 MDS (EAQMDS) 码的构建引起了极大的兴趣。在本文中，对于任意素数幂 q ，我们构造了两个新的 MDS Hermitian LCD 码族，长度为 n = q 2 + 1 λ $n=\frac {{{q^{2}}+1}}{\lambda }$ and n = q 2 − 1 r , $n=\frac {q^{2}-1}{r},$ where rq + 1. 通过将获得的 MDS Hermitian LCD 代码应用于 EAQMDS 代码，我们推导出参数 q 2 + 1 λ , q 2 + 1 λ − l + 1 , l 的新最大纠缠 EAQMDS 代码；l − 1 q ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}}+1}}{\lambda },\frac {{{q^{2}}+ 1}}{\lambda }-l+1,l;l-1}\right ] \kern -0.30em\right ]_{q}}$ 其中 2 ≤ l ≤ q 2 + 1 + 2 λ 2 λ $2 \leq l\leq \left \lfloor \frac {{{q^{2}}+1+2\lambda }}{2\lambda }\right \rfloor $ 和 q 2 − 1 r , q 2 − 1 r − γ , γ + 1 ; γ q ${\left [ \kern -0.30em\left [ {\frac {{{q^{2}-}1}}{r},\frac {{{q^{2}-}1}} {r} -\gamma ,\gamma +1;\gamma }\right ] \kern -0.30em\right ]_{q}}$ 其中 1 ≤ γ ≤ q 2 − 1 2 r 。$1\leq \gamma \leq \frac {{{q^{2}}-1}}{2r}.$