  We define a statistical measure of the typical size of short words in a
linear code over a finite field. We prove that the dual toric codes coming from
polytopes of degree one are characterized, among all dual toric codes, by being
extremal with respect to this measure. We also give a geometric interpretation
of the minimum distance of dual toric codes and characterize its extremal
values. Finally, we obtain formulas for the parameters of both primal and dual
toric codes associated to polytopes of degree one.
