Vol. 14, No. 4, 2021

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Classifying toric surface codes of dimension 7

Emily Cairncross, Stephanie Ford, Eli Garcia and Kelly Jabbusch

Vol. 14 (2021), No. 4, 605–616
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. In this note, we correct an error in the classification of the k = 7 case started by Hussain et al. (Comm. Anal. Geom. 28:2 (2020), 263–319) and disprove one of their conjectures.

Keywords
toric varieties, toric code, monomially equivalent, minimum distance
Mathematical Subject Classification
Primary: 94B27
Secondary: 14M25, 52B20
Milestones
Received: 22 May 2020
Revised: 20 May 2021
Accepted: 2 June 2021
Published: 23 October 2021

Communicated by Ravi Vakil
Authors
Emily Cairncross
Oberlin College
Oberlin, OH
United States
Stephanie Ford
Texas A&M
College Station, TX
United States
Eli Garcia
M.I.T.
Cambridge, MA
United States
Kelly Jabbusch
Department of Mathematics and Statistics
University of Michigan
Dearborn, MI
United States