The hull of a linear code over finite fields is the intersection of the code and its dual code, which has been widely studied due to its wide applications. In this paper, we develop a general method for constructing linear codes with small hulls using the eigenvalues of the generator matrices. Using this method, we construct many optimal Euclidean and Hermitian LCD codes, which improve the previously known lower bound on the largest minimum distance. We also obtain many (near) MDS LCD codes and (near) MDS codes with one-dimensional hull. Furthermore, we give three tables about formally self-dual LCD codes.

中文翻译：

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一种构造小壳形式自对偶码的改进方法

有限域上线性码的壳是该码及其对偶码的交集，由于其应用广泛而受到广泛研究。在本文中，我们开发了一种使用生成矩阵的特征值构造具有小外壳的线性码的通用方法。使用这种方法，我们构造了许多最优的欧几里德和厄尔米特 LCD 代码，这些代码改进了先前已知的最大最小距离的下限。我们还获得了许多（接近）MDS LCD 代码和（接近）具有一维外壳的 MDS 代码。此外，我们还给出了三张关于形式自对偶 LCD 代码的表格。