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.

翻译：本文研究了在基域上定义的线性自同态下保持稳定的线性码的秩重量层次结构，特别关注自同态为循环的情形。在后一种情况下，我们给出了此类码的第一秩重量等于$1$的充要条件（用其生成多项式表示），并推导了其最后秩重量的显式计算公式。