Toric Surface Codes and Minkowski Length of Polygons

Ivan Soprunov; Jenya Soprunova

doi:10.1137/080716554

Toric Surface Codes and Minkowski Length of Polygons

Ivan Soprunov, Jenya Soprunova

Kent State University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.

Original language	American English
Journal	SIAM Journal on Discrete Mathematics
Volume	23
DOIs	https://doi.org/10.1137/080716554
State	Published - Jan 1 2009

Keywords

evaluation codes
toric codes
Minkowski sum

Disciplines

Mathematics

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10.1137/080716554License: CC BY

Toric Surface Codes and Minkowski Length of PolygonsFinal published version, 837 KBLicense: CC BY

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title = "Toric Surface Codes and Minkowski Length of Polygons",

abstract = " In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.",

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AU - Soprunov, Ivan

AU - Soprunova, Jenya

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N2 - In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.

AB - In this paper we prove new lower bounds for the minimum distance of a toric surface code CP defined by a convex lattice polygon P⊂R2. The bounds involve a geometric invariant L(P), called the full Minkowski length of P. We also show how to compute L(P) in polynomial time in the number of lattice points in P.

KW - evaluation codes

KW - toric codes

KW - Minkowski sum

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/134

U2 - 10.1137/080716554

DO - 10.1137/080716554

M3 - Article

VL - 23

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

ER -

Toric Surface Codes and Minkowski Length of Polygons

Abstract

Keywords

Disciplines

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