About the generalized Hamming weights of matrix-product codes
<|reference_start|>About the generalized Hamming weights of matrix-product codes: 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.<|reference_end|>
@article{san-josé2024about,
    title={About the generalized Hamming weights of matrix-product codes},
    author={Rodrigo San-Jos'e},
    journal={arXiv preprint arXiv:2407.11810},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.11810},
    primaryClass={cs.IT math.IT}
}