We derive a general lower bound for the generalized Hamming weights of nested matrix-product codes, with a particular emphasis on the cases with two and three constituent codes. We also provide an upper bound which is reminiscent of the bounds used for the minimum distance of matrix-product codes. When the constituent codes are two Reed-Solomon codes, we obtain an explicit formula for the generalized Hamming weights of the resulting matrix-product code. We also deal with the non-nested case for the case of two constituent codes.

翻译：我们推导了嵌套矩阵乘积码广义汉明重量的一般下界，特别关注包含两个和三个分量码的情形。同时，我们给出了一个上界，该上界与矩阵乘积码最小距离的界具有相似形式。当分量码为两个里德-所罗门码时，我们得到了所得矩阵乘积码广义汉明重量的显式计算公式。此外，我们还针对两个分量码的情形讨论了非嵌套情况。