2025/09/25 by Amelia Gibbs, Gibbs, Amelia, Eliza Hogan +7
Computer Science · Mathematics · #14M25 #52B20 #94B27 (Primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2509.21178
openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Toric codes are error-correcting codes that are derived from toric varieties, which hold a unique correspondence to integral convex polytopes. In this paper, we focus on integral convex polytopes P ⊆ ℝ2 and the toric codes they define. We begin by studying period-1 polytopes -- polytopes satisfying the property L(tP) = tL(P) for all t ∈ ℤ+, where tP is the t-dilate of P, and we prove an explicit formula for the minimum distance of toric codes associated to a particular class of period-1 polytopes. We also apply the methods of Little and Schwarz, using Vandermonde matrices, to compute the minimum distance of another class of period-1 polytopes.