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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
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Abstract |
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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 by Hussain et al. (Comm. Anal. Geom. 28:2 (2020), 263–319) and disprove one of their conjectures. |
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Keywords
toric varieties, toric code, monomially equivalent, minimum
distance
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Mathematical Subject Classification
Primary: 94B27
Secondary: 14M25, 52B20
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Milestones
Received: 22 May 2020
Revised: 20 May 2021
Accepted: 2 June 2021
Published: 23 October 2021
Communicated by Ravi Vakil
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Authors |
| Emily Cairncross | |
| Oberlin College Oberlin, OH United States |
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| Stephanie Ford | |
| Texas A&M College Station, TX United States |
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| Eli Garcia | |
| M.I.T. Cambridge, MA United States |
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| Kelly Jabbusch | |
| Department of Mathematics and
Statistics University of Michigan Dearborn, MI United States |
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