Dual toric codes and polytopes of degree one

Valérie Gauthier Umaña, Mauricio Velasco

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

3 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)683-692
Número de páginas10
PublicaciónSIAM Journal on Discrete Mathematics
Volumen29
N.º1
DOI
EstadoPublicada - 2015
Publicado de forma externa

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