  In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a
deterministic algorithm for the unique decoding problem for polynomials of
bounded total degree over a general grid. We show that their algorithm can be
adapted to solve the unique decoding problem for the general family of Downset
codes. Here, a downset code is specified by a family D of monomials closed
under taking factors: the corresponding code is the space of evaluations of all
polynomials that can be written as linear combinations of monomials from D.
