Toric code distances from terraced polytopes

Abstract

We call a polytope terraced if upon projecting onto a one-dimensional coordinate space, each fiber of the projection is contained in the fiber below it. We present a technique to compute the minimum distance for toric codes arising from terraced polytopes. This technique is demonstrated by determining the minimum distance for all toric codes that correspond to smooth n –polytopes with n+2 facets. We also find the minimum distance for all toric codes coming from smooth polygons with five edges and from smooth polyhedra with six facets.