2021/03/31 by Tori Braun, James Carzon, Braun, Tori +5
Computer Science · Mathematics · #14M25 (Secondary) #94B27 (Primary) 52B20 #Advanced Data Storage Technologies #Algebraic Geometry (math.AG) #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #math.AG #msc:14M25 #msc:52B20 #msc:94B27
paper · pdf · doi:10.48550/arxiv.2103.16763
15 pages, 3 figures
arxiv created 2021/03/31 · openalex publication_date 2021/03/31 · arxiv updated 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 R3 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.