Lattice polytopes in coding theory
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum dist...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Yildiz Technical University
2015-05-01
|
| Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
| Subjects: | |
| Online Access: | http://eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2118 |
| id |
doaj-9630a1b77d2a4c24a50ea0d6bc9d4fea |
|---|---|
| record_format |
Article |
| spelling |
doaj-9630a1b77d2a4c24a50ea0d6bc9d4fea2020-11-24T21:06:39ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2015-05-0122859410.13069/jacodesmath.75353Lattice polytopes in coding theory Ivan Soprunov 0Department of Mathematics, Cleveland State UniversityIn this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include 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.http://eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2118Toric codeLattice polytopeMinkowski lengthSparse polynomials |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ivan Soprunov |
| spellingShingle |
Ivan Soprunov Lattice polytopes in coding theory Journal of Algebra Combinatorics Discrete Structures and Applications Toric code Lattice polytope Minkowski length Sparse polynomials |
| author_facet |
Ivan Soprunov |
| author_sort |
Ivan Soprunov |
| title |
Lattice polytopes in coding theory |
| title_short |
Lattice polytopes in coding theory |
| title_full |
Lattice polytopes in coding theory |
| title_fullStr |
Lattice polytopes in coding theory |
| title_full_unstemmed |
Lattice polytopes in coding theory |
| title_sort |
lattice polytopes in coding theory |
| publisher |
Yildiz Technical University |
| series |
Journal of Algebra Combinatorics Discrete Structures and Applications |
| issn |
2148-838X |
| publishDate |
2015-05-01 |
| description |
In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include 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. |
| topic |
Toric code Lattice polytope Minkowski length Sparse polynomials |
| url |
http://eds.yildiz.edu.tr/AjaxTool/GetArticleByPublishedArticleId?PublishedArticleId=2118 |
| work_keys_str_mv |
AT ivansoprunov latticepolytopesincodingtheory |
| _version_ |
1716765139539066880 |