  The moduli space of stable rational curves with marked points has two
distinguished families of maps: the forgetful maps, given by forgetting some of
the markings, and the Kapranov maps, given by complete linear series of
$\psi$-classes. The collection of all these maps embeds the moduli space into a
product of projective spaces. We call the multidegrees of this embedding
``Kapranov degrees,'' which include as special cases the work of Witten,
Silversmith, Gallet--Grasegger--Schicho, Castravet--Tevelev, Postnikov,
Cavalieri--Gillespie--Monin, and Gillespie--Griffins--Levinson. We establish,
in terms of a combinatorial matching condition, upper bounds for Kapranov
degrees and a characterization of their positivity. The positivity
characterization answers a question of Silversmith and gives a new proof of
Laman's theorem characterizing generically rigid graphs in the plane. We
achieve this by proving a recursive formula for Kapranov degrees and by using
tools from the theory of error correcting codes.
