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## A module minimization approach to Gabidulin decoding via interpolation

#### Anna-Lena Horlemann-Trautmann [1] , Margreta Kuijper [2]

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.
Gabidulin codes, Linearized polynomials, Interpolation, Minimal basis, Parametrization, Polynomial modules, Rank metric, Iterative algorithm
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Subjects Engineering Articles Orcid: 0000-0003-2685-2343Author: Anna-Lena Horlemann-Trautmann Orcid: 0000-0001-9223-9550Author: Margreta Kuijper (Primary Author) Publication Date : January 15, 2018
 Bibtex @research article { jacodesmath369863, journal = {Journal of Algebra Combinatorics Discrete Structures and Applications}, issn = {}, eissn = {2148-838X}, address = {}, publisher = {Yildiz Technical University}, year = {2018}, volume = {5}, pages = {29 - 43}, doi = {10.13069/jacodesmath.369863}, title = {A module minimization approach to Gabidulin decoding via interpolation}, key = {cite}, author = {Horlemann-trautmann, Anna-Lena and Kuijper, Margreta} } APA Horlemann-trautmann, A , Kuijper, M . (2018). A module minimization approach to Gabidulin decoding via interpolation . Journal of Algebra Combinatorics Discrete Structures and Applications , 5 (1) , 29-43 . DOI: 10.13069/jacodesmath.369863 MLA Horlemann-trautmann, A , Kuijper, M . "A module minimization approach to Gabidulin decoding via interpolation" . Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 29-43 Chicago Horlemann-trautmann, A , Kuijper, M . "A module minimization approach to Gabidulin decoding via interpolation". Journal of Algebra Combinatorics Discrete Structures and Applications 5 (2018 ): 29-43 RIS TY - JOUR T1 - A module minimization approach to Gabidulin decoding via interpolation AU - Anna-Lena Horlemann-trautmann , Margreta Kuijper Y1 - 2018 PY - 2018 N1 - doi: 10.13069/jacodesmath.369863 DO - 10.13069/jacodesmath.369863 T2 - Journal of Algebra Combinatorics Discrete Structures and Applications JF - Journal JO - JOR SP - 29 EP - 43 VL - 5 IS - 1 SN - -2148-838X M3 - doi: 10.13069/jacodesmath.369863 UR - https://doi.org/10.13069/jacodesmath.369863 Y2 - 2017 ER - EndNote %0 Journal of Algebra Combinatorics Discrete Structures and Applications A module minimization approach to Gabidulin decoding via interpolation %A Anna-Lena Horlemann-trautmann , Margreta Kuijper %T A module minimization approach to Gabidulin decoding via interpolation %D 2018 %J Journal of Algebra Combinatorics Discrete Structures and Applications %P -2148-838X %V 5 %N 1 %R doi: 10.13069/jacodesmath.369863 %U 10.13069/jacodesmath.369863 ISNAD Horlemann-trautmann, Anna-Lena , Kuijper, Margreta . "A module minimization approach to Gabidulin decoding via interpolation". Journal of Algebra Combinatorics Discrete Structures and Applications 5 / 1 (January 2018): 29-43 . https://doi.org/10.13069/jacodesmath.369863 AMA Horlemann-trautmann A , Kuijper M . A module minimization approach to Gabidulin decoding via interpolation. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 29-43. Vancouver Horlemann-trautmann A , Kuijper M . A module minimization approach to Gabidulin decoding via interpolation. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018; 5(1): 29-43.

Authors of the Article
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