Dual toric codes and polytopes of degree one

Valérie Gauthier Umaña, Mauricio Velasco

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)683-692
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Volume29
Issue number1
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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