A Basis for all Solutions of the Key Equation for Gabidulin Codes
Information Theory
2010-06-10 v1 math.IT
Abstract
We present and prove the correctness of an efficient algorithm that provides a basis for all solutions of a key equation in order to decode Gabidulin (G-) codes up to a given radius tau. This algorithm is based on a symbolic equivalent of the Euclidean Algorithm (EA) and can be applied for decoding of G-codes beyond half the minimum rank distance. If the key equation has a unique solution, our algorithm reduces to Gabidulin's decoding algorithm up to half the minimum distance. If the solution is not unique, we provide a basis for all solutions of the key equation. Our algorithm has time complexity O(tau^2) and is a generalization of the modified EA by Bossert and Bezzateev for Reed-Solomon codes.
Keywords
Cite
@article{arxiv.1006.1743,
title = {A Basis for all Solutions of the Key Equation for Gabidulin Codes},
author = {Antonia Wachter and Vladimir Sidorenko and Martin Bossert},
journal= {arXiv preprint arXiv:1006.1743},
year = {2010}
}
Comments
accepted for ISIT 2010, Austin, TX, USA