SIAM Journal on Discrete Mathematics
In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.
Soprunov, Ivan and Soprunova, Jenya, "Toric Surface Codes and Minkowski Length of Polygons" (2009). Mathematics Faculty Publications. 134.