Let R = F q 2 + uF q 2 , where F q 2 is the finite field with q 2 elements, q is a power of a prime p, and u 2 = 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 F q 2 as Gray images of linear and constacyclic codes of length n over R. By using the explicit symplectic method in [9], we get the desired maximal entanglement EAQECCs.
<p style='text-indent:20px;'>Linear complementary dual (LCD) codes have wide applications in data storage, communications systems and cryptography. In this paper, we introduce a concept of LCD codes in the metric space <inline-formula><tex-math id="M1">\begin{document}$ Mat_{n, s}(\mathbb{F}_{q}) $\end{document}</tex-math></inline-formula> endowed with the Niederreiter-Rosenbloom-Tsfasman metric (NRT metric), which are called Niederreiter-Rosenbloom-Tsfasman LCD (NRT LCD) codes. NRT LCD codes introduced in this paper are actually a generalization of Euclidean LCD codes. For <inline-formula><tex-math id="M2">\begin{document}$ s = 1 $\end{document}</tex-math></inline-formula>, an NRT LCD code is just an Euclidean LCD code. A necessary and sufficient condition for an NRT linear code to be an NRT LCD code is provided. Also, the existence of NRT LCD codes is investigated and some constructions of NRT LCD codes and NRT LCD MDS codes are discussed.</p>
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