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

26 Scopus citations

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. © 2008 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	384-400
Number of pages	17
Journal	SIAM Journal on Discrete Mathematics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1137/080716554
State	Published - Dec 1 2008

Keywords

Evaluation codes
Minkowski sum
Toric codes

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10.1137/080716554

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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. {\textcopyright} 2008 Society for Industrial and Applied Mathematics.",

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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. © 2008 Society for Industrial and Applied Mathematics.

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KW - Minkowski sum

KW - Toric codes

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Toric surface codes and Minkowski length of polygons

Abstract

Keywords

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