Dual Toric Codes and Polytopes of Degree One
| Autor: | Mauricio Velasco, Valérie Gauthier Umaña |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
General Mathematics
Codes over finite fields Polytope Topology Measure (mathematics) Interpretation (model theory) Combinatorics Mathematics - Algebraic Geometry Linear codes Minimal degree Varieties of minimal degree Exact formulas Mathematics::Algebraic Geometry Geometric interpretation Statistical measures 14G50 14M25 94B27 Minimum distance Mathematics::Symplectic Geometry Mathematics Discrete mathematics Mathematics::Commutative Algebra Degree (graph theory) Toric variety Codes (symbols) Toric varieties Linear code Dual (category theory) Finite field Finite fields |
| Zdroj: | Repositorio EdocUR-U. Rosario Universidad del Rosario instacron:Universidad del Rosario |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/140966228 |
| Popis: | 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. Comment: 13 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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