论文标题
来自循环代码的两个纠缠辅助量子MDS代码的家族
Two families of Entanglement-assisted Quantum MDS Codes from cyclic Codes
论文作者
论文摘要
使用纠缠辅助（EA）形式主义，允许任意经典的线性代码通过使用发送方和接收器之间的预共享纠缠转换为EAQECC。在本文中，基于经典的循环MDS代码，通过利用前共享的最大纠缠状态，我们构建了两个$ q $ - ar-ar-ary纠缠的量子量子MDS代码$ [[\ frac {q^{2} +1} +1} +1} {a} {a} {a} Q是$ am+l $的形式的主要功率，$ a =（l^2+1）$或$ a = \ frac {（l^2+1）} {5} $。我们表明，所有$ q $ -ary EAQMD的最小距离上限都比已知长度的已知量子MD（QMDS）代码大得多。这些$ q $ -ary eaqmds代码中的大多数都是新的，因为它们的参数未被文献中可用的代码涵盖。
With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.
