Reference: $d_r(\mathcal{C}_m)\geq \delta_{FR}^{r}(m)$ Generalized Feng-Rao distance is lower bound of generalized Hamming Weight

Question

I am looking for a reference (article/book), where they give a proof for this claim:

$$d_r(\mathcal{C}_m)\geq \delta_{FR}^{r}(m)$$

Where $\mathcal{C}_m$ is the $m^{th}$ classical one point algebraic code, $d_r(\mathcal{C}_m)$ is the generalized Hamming weight of order $r$ for that code, and $\delta_{FR}^{r}(m)$ is the $r$ generalized Feng-Rao distance of $m$.

Answer 1

For those interested, the best I could find is in the original paper, Theorem 3.14:

Petra Heijnen and Ruud Pellikaan. Generalized Hamming weights of q-ary Reed-Muller codes. 1998

https://www.win.tue.nl/~ruudp/paper/29.pdf