Toric surface codes and Minkowski length of polygons

TL;DR

This paper establishes new lower bounds for the minimum distance of toric surface codes using a geometric invariant called the full Minkowski length, which can be computed for any convex lattice polygon.

Contribution

It introduces the full Minkowski length as a novel geometric invariant to bound the minimum distance of toric surface codes.

Findings

New lower bounds for minimum distance of toric surface codes

Full Minkowski length can be efficiently computed for any polygon

Enhanced understanding of geometric properties influencing code performance

Abstract

In this paper we prove new lower bounds for the minimum distance of a toric surface code defined by a convex lattice polygon P. The bounds involve a geometric invariant L(P), called the full Minkowski length of P which can be easily computed for any given P.