  Toric codes are evaluation codes obtained from an integral convex polytope $P
\subset \R^n$ and finite field $\F_q$. They are, in a sense, a natural
extension of Reed-Solomon codes, and have been studied recently by J. Hansen
and D. Joyner. In this paper, we obtain upper and lower bounds on the minimum
distance of a toric code constructed from a polygon $P \subset \R^2$ by
examining Minkowski sum decompositions of subpolygons of $P$. Our results give
a simple and unifying explanation of bounds of Hansen and empirical results of
Joyner; they also apply to previously unknown cases.
