We provide methods and algorithms to construct Hermitian linear complementary dual (LCD) codes over finite fields. We study existence of self-dual basis with respect to Hermitian inner product, and as an application, we construct Euclidean LCD codes by projecting the Hermitian codes over such a basis. Many optimal quaternary Hermitian and ternary Euclidean LCD codes are obtained. Comparisons with classical constructions are made.

中文翻译：

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在Hermitian LCD代码及其灰度图像上

我们提供了在有限域上构造Hermitian线性互补对偶（LCD）代码的方法和算法。我们研究关于Hermitian内积的自对偶基础的存在，并作为应用，通过在这样的基础上投影Hermitian代码来构造欧几里得LCD代码。获得了许多最优的四元Hermitian和三元欧几里得LCD代码。与经典结构进行了比较。