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About the generalized Hamming weights of matrix-product codes
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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.
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Cited by 1 Pith paper
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The weight hierarchy of decreasing norm-trace codes
The complete weight hierarchy of every decreasing norm-trace code is determined by a footprint maximization, recovering the Hermitian hierarchy as a special case.
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