  Motivated by the current research of generalized symmetries and the
construction of conserved charges in pure Einstein gravity linearized over
Minkowski spacetime in Cartesian coordinates, we investigate, from a purely
classical point of view, the construction of these charges in a coordinate- and
frame-independent language in order to generalize them further. We show that
all the charges constructed in that context are associated to the conformal
Killing-Yano 2-forms of Minkowski spacetime. Furthermore, we prove that those
associated to closed conformal Killing-Yano 2-forms are identical to the
charges constructed by Kastor and Traschen for their dual Killing-Yano
(d-2)-forms. We discuss the number of independent and non-trivial gravitational
charges that can be constructed in this way.
