On the structure of generalized toric codes

Diego Ruano Benito

doi:10.1016/j.jsc.2007.07.018

On the structure of generalized toric codes

Diego Ruano Benito

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

20 Citationer (Scopus)

Abstract

Udgivelsesdato: May

Originalsprog	Engelsk
Tidsskrift	Journal of Symbolic Computation
Vol/bind	44
Udgave nummer	5
Sider (fra-til)	499-506
ISSN	0747-7171
DOI	https://doi.org/10.1016/j.jsc.2007.07.018
Status	Udgivet - 2009
Udgivet eksternt	Ja

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10.1016/j.jsc.2007.07.018

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@article{e4987fe0c78911debcee000ea68e967b,

title = "On the structure of generalized toric codes",

abstract = "Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so-called generalized toric codes. This extension consists of evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance.",

author = "Benito, {Diego Ruano}",

year = "2009",

doi = "10.1016/j.jsc.2007.07.018",

language = "English",

volume = "44",

pages = "499--506",

journal = "Journal of Symbolic Computation",

issn = "0747-7171",

publisher = "Academic Press",

number = "5",

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TY - JOUR

T1 - On the structure of generalized toric codes

AU - Benito, Diego Ruano

PY - 2009

Y1 - 2009

N2 - Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so-called generalized toric codes. This extension consists of evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance.

AB - Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so-called generalized toric codes. This extension consists of evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance.

U2 - 10.1016/j.jsc.2007.07.018

DO - 10.1016/j.jsc.2007.07.018

M3 - Journal article

SN - 0747-7171

VL - 44

SP - 499

EP - 506

JO - Journal of Symbolic Computation

JF - Journal of Symbolic Computation

IS - 5

ER -

On the structure of generalized toric codes

Abstract

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