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Indecomposable polyhedra and toric codes

MSRI-UP 2009: Coding Theory June 15, 2009 - July 24, 2009

July 24, 2009 (02:30 PM PDT - 03:30 PM PDT)
Speaker(s): Aileen Gaudinez, Cheryl Outing, Rachel Vega
Location: MSRI: Simons Auditorium
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Abstract

In this report we describe and classify indecomposable lattice polytopes in R 3 . This paper explores some indecomposable polyhedra not yet considered, and also introduces an idea of “family”. We investigate the toric codes over the Galois Field F8 that are constructed by these polyhedra, following the original method of constructing toric codes from polytopes by Hansen. In addition, we conjecture equivalence relations between the members of a determined family and subsequently the toric codes they generate.

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