A module minimization approach to Gabidulin decoding via interpolation

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Anna-Lena Horlemann-Trautmann¹  Margreta Kuijper² 

[1] Faculty of Mathematics and Statistics, University of St. Gallen;Department of Electrical and Electronic Engineering, University of Melbourne

关键词: Gabidulin codes;    Linearized polynomials;    Interpolation;    Minimal basis;    Parametrization;    Polynomial modules;    Rank metric;    Iterative algorithm;   

DOI  :  10.13069/jacodesmath.369863

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

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.

【 授权许可】

CC BY