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On the rank weight hierarchy of $M$-codes
G. Berhuy, J. Molina · 2025-07-01 · via cs.IT updates on arXiv.org

We study the rank weight hierarchy of linear codes which are stable under a linear endomorphism defined over the base field, in particular when the endomorphism is cyclic. In this last case, we give a necessary and sufficient condition for such a code to have first rank weight equal to $1$ in terms of its generator polynomial, as well as an explicit formula for its last rank weight.

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