Lattice Polytopes in Coding Theory

Ivan Soprunov

doi:10.13069/jacodesmath.75353

Lattice Polytopes in Coding Theory

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Abstract

In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.

Original language	American English
Journal	Journal of Algebra Combinatorics Discrete Structures and Applications
Volume	2
DOIs	https://doi.org/10.13069/jacodesmath.75353
State	Published - Jan 1 2015

Keywords

toric code
lattice polytope
Minkowski length
sparse polynomials.

Disciplines

Mathematics

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10.13069/jacodesmath.75353License: CC BY

Lattice Polytopes in Coding TheoryFinal published version, 1.01 MBLicense: CC BY

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title = "Lattice Polytopes in Coding Theory",

abstract = " In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.",

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author = "Ivan Soprunov",

year = "2015",

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language = "American English",

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journal = "Journal of Algebra Combinatorics Discrete Structures and Applications",

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T1 - Lattice Polytopes in Coding Theory

AU - Soprunov, Ivan

PY - 2015/1/1

Y1 - 2015/1/1

N2 - In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.

AB - In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also prove a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.

KW - toric code

KW - lattice polytope

KW - Minkowski length

KW - sparse polynomials.

UR - https://engagedscholarship.csuohio.edu/scimath_facpub/280

U2 - 10.13069/jacodesmath.75353

DO - 10.13069/jacodesmath.75353

M3 - Article

VL - 2

JO - Journal of Algebra Combinatorics Discrete Structures and Applications

JF - Journal of Algebra Combinatorics Discrete Structures and Applications

ER -

Lattice Polytopes in Coding Theory

Abstract

Keywords

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