English

Classifying toric surface codes of dimension $7$

Algebraic Geometry 2021-11-03 v3

Abstract

Toric surface codes are a class of error-correcting codes coming from a lattice polytope defining a two-dimensional toric variety. Previous authors have mostly completed classifications of these toric surface codes with dimension up to k=7.k = 7. In this note, we correct an error in the classification of the k=7k=7 case started in \cite{HLYZZ}, and disprove one of their conjectures.

Cite

@article{arxiv.2009.09821,
  title  = {Classifying toric surface codes of dimension $7$},
  author = {Emily Cairncross and Stephanie Ford and Eli Garcia and Kelly Jabbusch},
  journal= {arXiv preprint arXiv:2009.09821},
  year   = {2021}
}

Comments

Final version

R2 v1 2026-06-23T18:41:16.557Z