Efficient Decoding of Gabidulin Codes over Galois Rings
Information Theory
2021-02-04 v1 math.IT
Abstract
This paper presents the first decoding algorithm for Gabidulin codes over Galois rings with provable quadratic complexity. The new method consists of two steps: (1) solving a syndrome-based key equation to obtain the annihilator polynomial of the error and therefore the column space of the error, (2) solving a key equation based on the received word in order to reconstruct the error vector. This two-step approach became necessary since standard solutions as the Euclidean algorithm do not properly work over rings.
Keywords
Cite
@article{arxiv.2102.02157,
title = {Efficient Decoding of Gabidulin Codes over Galois Rings},
author = {Sven Puchinger and Julian Renner and Antonia Wachter-Zeh and Jens Zumbrägel},
journal= {arXiv preprint arXiv:2102.02157},
year = {2021}
}