  Affine Cartesian codes are defined by evaluating multivariate polynomials at
a cartesian product of finite subsets of a finite field. In this work we
examine properties of these codes as batch codes. We consider the recovery sets
to be defined by points aligned on a specific direction and the buckets to be
derived from cosets of a subspace of the ambient space of the evaluation
points. We are able to prove that under these conditions, an affine Cartesian
code is able to satisfy a query of size up to one more than the dimension of
the space of the ambient space.
