TL;DR
This paper explores the combinatorial properties of lattice polytopes in relation to toric codes, introducing new bounds and formulas for their minimum distance, advancing the understanding of their structure and performance.
Contribution
It presents a new inductive bound for the minimum distance of generalized toric codes and derives formulas for specific lattice point configurations.
Findings
New inductive bound for minimum distance of generalized toric codes
Formulas for minimum distance in special lattice configurations
Enhanced understanding of lattice polytope combinatorics in coding theory
Abstract
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.