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Appl. Math."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>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\u2013Solomon codes, we obtain an explicit formula for the generalized Hamming weights of the resulting matrix-product code. 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