Toric code distances from terraced polytopes

Abstract

We call a polytope terraced if upon projecting onto a one-dimensional coordinate space, each fiber ofthe projection is contained in the fiber below it. We present a technique to compute the minimumdistance for toric codes arising from terraced polytopes. This technique is demonstrated by determining the minimum distance for all toric codes that correspond to smoothn–polytopes with $n+ 2$ facets. We also find the minimum distance for all toric codes coming from smooth polygons with fiveedges and from smooth $3$–polytopes with six facets.

Received: 18 August 2021 | Accepted: 20 January 2022