Dual toric codes and polytopes of degree one

We define a statistical measure of the typical size of words of low weight 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 geomet...

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Autores Principales: Umaña V.G., Velasco M.
Formato: Artículo (Article)
Lenguaje:Inglés (English)
Publicado: Society for Industrial and Applied Mathematics Publications 2015
Materias:
Acceso en línea:https://repository.urosario.edu.co/handle/10336/23299
https://doi.org/10.1137/140966228
id ir-10336-23299
recordtype dspace
spelling ir-10336-232992022-05-02T12:37:20Z Dual toric codes and polytopes of degree one Umaña V.G. Velasco M. Topology Exact formulas Finite fields Geometric interpretation Linear codes Minimal degree Minimum distance Statistical measures Toric varieties Codes (symbols) Codes over finite fields Toric varieties Varieties of minimal degree We define a statistical measure of the typical size of words of low weight 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 exact formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one. © 2015 Society for Industrial and Applied Mathematics. 2015 2020-05-26T00:01:00Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 10957146 08954801 https://repository.urosario.edu.co/handle/10336/23299 https://doi.org/10.1137/140966228 eng info:eu-repo/semantics/openAccess application/pdf Society for Industrial and Applied Mathematics Publications instname:Universidad del Rosario
institution EdocUR - Universidad del Rosario
collection DSpace
language Inglés (English)
topic Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
spellingShingle Topology
Exact formulas
Finite fields
Geometric interpretation
Linear codes
Minimal degree
Minimum distance
Statistical measures
Toric varieties
Codes (symbols)
Codes over finite fields
Toric varieties
Varieties of minimal degree
Umaña V.G.
Velasco M.
Dual toric codes and polytopes of degree one
description We define a statistical measure of the typical size of words of low weight 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 exact formulas for the parameters of both primal and dual toric codes associated to polytopes of degree one. © 2015 Society for Industrial and Applied Mathematics.
format Artículo (Article)
author Umaña V.G.
Velasco M.
author_facet Umaña V.G.
Velasco M.
author_sort Umaña V.G.
title Dual toric codes and polytopes of degree one
title_short Dual toric codes and polytopes of degree one
title_full Dual toric codes and polytopes of degree one
title_fullStr Dual toric codes and polytopes of degree one
title_full_unstemmed Dual toric codes and polytopes of degree one
title_sort dual toric codes and polytopes of degree one
publisher Society for Industrial and Applied Mathematics Publications
publishDate 2015
url https://repository.urosario.edu.co/handle/10336/23299
https://doi.org/10.1137/140966228
_version_ 1740172705395638272
score 12,131701