A census of two-dimensional toric codes over Galois fields of sizes 7, 8 and 9

J. Hansen introduced toric codes using the geometry of polygons in R 2 and the convex polytopes P in R m more generally. But collections of points more general than the sets P ∩Z m can also be used to define generalized toric codes. In our research using the Magma computer algebra system, we search to find the generalized toric codes with the best parameters for some dimensions over the Galois fields of size 7, 8 and 9.