Many classical constructions, such as Plotkin's and Turyn's, were generalized by matrix product (MP) codes. Quasi-twisted (QT) codes, on the other hand, form an algebraically rich structure class that contains many codes with best-known parameters. We significantly extend the definition of MP codes to establish a broader class of generalized matrix product (GMP) codes that contains QT codes as well. We propose a generator matrix formula for any linear GMP code and provide a condition for determining the code size. We prove that any QT code has a GMP structure. Then we show how to build a generator polynomial matrix for a QT code from its GMP structure, and vice versa. Despite that the class of QT codes contains many codes with best-known parameters, we present different examples of GMP codes with best-known parameters that are neither MP nor QT. Two different lower bounds on the minimum distance of GMP codes are presented; they generalize their counterparts in the MP codes literature. The second proposed lower bound replaces the non-singular by columns matrix with a less restrictive condition. Some examples are provided for comparing the two proposed bounds, as well as showing that these bounds are tight.

翻译：许多经典构造（如Plotkin和Turyn构造）已被矩阵乘积（MP）码推广。另一方面，准扭曲（QT）码构成一个代数结构丰富的码类，包含许多具有最佳已知参数的码。我们大幅扩展了MP码的定义，建立了一个更广泛的广义矩阵乘积（GMP）码类，其中也包含QT码。我们为任意线性GMP码提出了一个生成矩阵公式，并给出了确定码规模的充分条件。我们证明任意QT码都具有GMP结构，进而展示如何从QT码的GMP结构构建其生成多项式矩阵，反之亦然。尽管QT码类包含许多具有最佳已知参数的码，我们仍给出了若干既非MP也非QT的GMP码实例，这些码同样具有最佳已知参数。本文提出了两个不同的GMP码最小距离下界，它们推广了MP码文献中的对应下界。第二个下界将非奇异列矩阵替换为限制条件更宽松的矩阵。通过若干实例对两个下界进行比较，并证明这些下界是紧的。