On the rank weight hierarchy of $M$-codes
Information Theory
2026-02-02 v3 math.IT
Abstract
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 in terms of its generator polynomial, as well as an explicit formula for its last rank weight.
Cite
@article{arxiv.2507.00609,
title = {On the rank weight hierarchy of $M$-codes},
author = {G. Berhuy and J. Molina},
journal= {arXiv preprint arXiv:2507.00609},
year = {2026}
}