In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {general} dual-containing matrix-product code; the second one is founded on {a specific family of} matrices, where we provide an efficient algorithm for generating them {on the basis of Toeplitz matrices} and {it has an interesting application in producing new non-singular by columns quasi-unitary matrices}; and the last two ones are based on the utilization of certain special Toeplitz matrices. Concrete examples and detailed comparisons are provided. As a byproduct, we also find an application of Toeplitz matrices, which is closely related to the constructions of quantum codes.

翻译：本文提出了四种与Toeplitz矩阵相关的广义自正交矩阵乘积码的构造方法。第一种方法基于已知的广义对偶包含矩阵乘积码的对偶码；第二种方法建立在特定矩阵族的基础上，我们提供了一种基于Toeplitz矩阵的高效生成算法，该算法在产生新的非奇异列拟酉矩阵方面具有重要应用；最后两种方法则基于特定特殊Toeplitz矩阵的运用。文中给出了具体算例与详细比较分析。作为副产品，我们还发现了Toeplitz矩阵在量子码构造中的重要应用。