Classifying toric surface codes of dimension $7$
Emily Cairncross, Stephanie Ford, Eli Garcia, Kelly Jabbusch
TL;DR
This paper corrects a classification error and disproves a conjecture related to toric surface codes of dimension 7, advancing the understanding of these error-correcting codes derived from lattice polytopes.
Contribution
It provides a corrected classification of toric surface codes for dimension 7 and refutes a previous conjecture, refining the theoretical framework.
Findings
Corrected the classification of toric surface codes for dimension 7
Disproved a previously held conjecture about these codes
Enhanced understanding of the structure of toric surface codes
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 In this note, we correct an error in the classification of the case started in \cite{HLYZZ}, and disprove one of their conjectures.
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