In 2001, Blackmore and Norton introduced an important tool called matrix-product codes, which turn out to be very useful to construct new quantum codes of large lengths. To obtain new and good quantum codes, we first give a general approach to construct matrix-product codes being Hermitian dual-containing and then provide the constructions of such codes in the case \(s{\mid }(q^{2}-1)\), where s is the number of the constituent codes in a matrix-product code. For \(s{\mid } (q+1)\), we construct such codes with lengths more flexible than the known ones in the literature. For \(s{\mid } (q^{2}-1)\) and \(s{\not \mid } (q+1)\), such codes are constructed in an unusual manner; some of the constituent codes therein are not required to be Hermitian dual-containing. Accordingly, by Hermitian construction, we present two procedures for acquiring quantum codes. Finally, we list some good quantum codes, many of which improve those available in the literature or add new parameters.

在2001年，Blackmore和Norton引入了一种重要的工具，称为矩阵乘积码，它对于构造新的大长度量子码非常有用。为了获得新的和好的量子码，我们首先给出一种通用的方法来构造包含Hermitian对偶的矩阵乘积码，然后在\（s {\ mid}（q ^ {2}- 1）\），其中s是矩阵乘积代码中组成代码的数量。对于\（s {\ mid}（q + 1）\），我们构造这样的代码，其长度比文献中的已知代码更灵活。对于\（s {\ mid}（q ^ {2} -1）\）和\（s {\ not \ mid}（q + 1）\），此类代码的构建方式很特殊；其中的一些组成代码不需要是Hermitian对偶的。因此，通过厄米构造，我们提出了两种获取量子码的程序。最后，我们列出了一些好的量子代码，其中许多改进了文献中可用的量子代码或添加了新参数。