  In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS
codes as a generalization of MDS codes. An order-$\ell$ MDS code, denoted by
$\operatorname{MDS}(\ell)$, has the property that any $\ell$ subspaces formed
from columns of its generator matrix intersect as minimally as possible. An
independent work by Roth defined a different notion of higher order MDS codes
as those achieving a generalized singleton bound for list-decoding. In this
work, we show that these two notions of higher order MDS codes are (nearly)
equivalent.
  We also show that generic Reed-Solomon codes are $\operatorname{MDS}(\ell)$
for all $\ell$, relying crucially on the GM-MDS theorem which shows that
generator matrices of generic Reed-Solomon codes achieve any possible zero
pattern. As a corollary, this implies that generic Reed-Solomon codes achieve
list decoding capacity. More concretely, we show that, with high probability, a
random Reed-Solomon code of rate $R$ over an exponentially large field is list
decodable from radius $1-R-\epsilon$ with list size at most
$\frac{1-R-\epsilon}{\epsilon}$, resolving a conjecture of Shangguan and Tamo.
