A module minimization approach to Gabidulin decoding via interpolation

A module minimization approach to Gabidulin decoding via interpolation

We focus on iterative interpolation-based decoding of Gabidulin codes and present an algorithm that computes a minimal basis for an interpolation module. We extend existing results for Reed-Solomon codes in showing that this minimal basis gives rise to a parametrization of elements in the module tha...

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Main Authors: Anna-Lena Horlemann-Trautmann, Margreta Kuijper
Format: Article
Language:English
Published: Yildiz Technical University 2017-12-01
Series:Journal of Algebra Combinatorics Discrete Structures and Applications
Online Access:http://jacodesmath.com/index.php/jacodesmath/article/view/83
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spelling doaj-518f84dc3fa140c98b9e8a06809a27be2020-11-24T22:13:29ZengYildiz Technical UniversityJournal of Algebra Combinatorics Discrete Structures and Applications2148-838X2017-12-0151100A module minimization approach to Gabidulin decoding via interpolationAnna-Lena Horlemann-Trautmann0Margreta Kuijper1Algorithmics Laboratory EPFL LausanneUniversity of MelbourneWe focus on iterative interpolation-based decoding of Gabidulin codes and present an algorithm that computes a minimal basis for an interpolation module. We extend existing results for Reed-Solomon codes in showing that this minimal basis gives rise to a parametrization of elements in the module that lead to all Gabidulin decoding solutions that are at a fixed distance from the received word. Our module-theoretic approach strengthens the link between Gabidulin decoding and Reed-Solomon decoding, thus providing a basis for further work into Gabidulin list decoding.http://jacodesmath.com/index.php/jacodesmath/article/view/83
collection DOAJ
language English
format Article
sources DOAJ
author Anna-Lena Horlemann-Trautmann
Margreta Kuijper
spellingShingle Anna-Lena Horlemann-Trautmann
Margreta Kuijper
A module minimization approach to Gabidulin decoding via interpolation
Journal of Algebra Combinatorics Discrete Structures and Applications
author_facet Anna-Lena Horlemann-Trautmann
Margreta Kuijper
author_sort Anna-Lena Horlemann-Trautmann
title A module minimization approach to Gabidulin decoding via interpolation
title_short A module minimization approach to Gabidulin decoding via interpolation
title_full A module minimization approach to Gabidulin decoding via interpolation
title_fullStr A module minimization approach to Gabidulin decoding via interpolation
title_full_unstemmed A module minimization approach to Gabidulin decoding via interpolation
title_sort module minimization approach to gabidulin decoding via interpolation
publisher Yildiz Technical University
series Journal of Algebra Combinatorics Discrete Structures and Applications
issn 2148-838X
publishDate 2017-12-01
description We focus on iterative interpolation-based decoding of Gabidulin codes and present an algorithm that computes a minimal basis for an interpolation module. We extend existing results for Reed-Solomon codes in showing that this minimal basis gives rise to a parametrization of elements in the module that lead to all Gabidulin decoding solutions that are at a fixed distance from the received word. Our module-theoretic approach strengthens the link between Gabidulin decoding and Reed-Solomon decoding, thus providing a basis for further work into Gabidulin list decoding.
url http://jacodesmath.com/index.php/jacodesmath/article/view/83
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AT margretakuijper amoduleminimizationapproachtogabidulindecodingviainterpolation
AT annalenahorlemanntrautmann moduleminimizationapproachtogabidulindecodingviainterpolation
AT margretakuijper moduleminimizationapproachtogabidulindecodingviainterpolation
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