Classifying toric 3-fold codes of dimensions 4 and 5

A toric code is an error-correcting code determined by a toric variety or its associated integral convex polytope. We investigate \(4\)- and \(5\)-dimensional toric \(3\)-fold codes, which are codes arising from polytopes in \(\mathbf{R}^3\) with four and five lattice points, respectively. By comput...

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Bibliographic Details
Published in:arXiv.org 2021-03
Main Authors: Braun, Tori, Carzon, James, Gorham, Jenna, Jabbusch, Kelly
Format: Article
Language:English
Subjects:
Classification
Codes
Error correcting codes
Error correction
Polytopes
Online Access:Get full text
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Summary:A toric code is an error-correcting code determined by a toric variety or its associated integral convex polytope. We investigate \(4\)- and \(5\)-dimensional toric \(3\)-fold codes, which are codes arising from polytopes in \(\mathbf{R}^3\) with four and five lattice points, respectively. By computing the minimum distances of each code, we fully classify the \(4\)-dimensional codes. We further present progress toward the same goal for dimension \(5\) codes. In particular, we classify the \(5\)-dimensional toric \(3\)-fold codes arising from polytopes of width 1.
ISSN:2331-8422