2014/04/15 by Valérie Gauthier Uman͂a, Valérie Gauthier Umaña, Umaña, Valérie Gauthier +2
Computer Science · Mathematics · #14G50 #14M25 #94B27 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Mathematics #math.AG #msc:14G50 #msc:14M25 #msc:94B27 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1404.4063
13 pages
arxiv created 2014/04/15 · openalex publication_date 2014/04/15 · arxiv updated 2014/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a statistical measure of the typical size of short words in a linear code over a finite field. We prove that the dual toric codes coming from polytopes of degree one are characterized, among all dual toric codes, by being extremal with respect to this measure. We also give a geometric interpretation of the minimum distance of dual toric codes and characterize its extremal values. Finally, we obtain formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one.