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23.03.2016 | Ausgabe 1-2/2017

# Algebraic decoding of folded Gabidulin codes

Zeitschrift:
Designs, Codes and Cryptography > Ausgabe 1-2/2017
Autoren:
Wichtige Hinweise
This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.

## Abstract

An efficient interpolation-based decoding algorithm for $$h$$-folded Gabidulin codes is presented that can correct rank errors beyond half the minimum rank distance for any code rate $$0\le R\le 1$$. The algorithm serves as a list decoder or as a probabilistic unique decoder and improves upon existing schemes, especially for high code rates. A probabilistic unique decoder with adjustable decoding radius is presented. The decoder outputs a unique solution with high probability and requires at most $$\mathcal {O}({s^2n^2})$$ operations in $$\mathbb {F}_{q^m}$$, where $$1\le s\le h$$ is a decoding parameter and $$n\le m$$ is the length of the unfolded code over $$\mathbb {F}_{q^m}$$. An upper bound on the average list size of folded Gabidulin codes and on the decoding failure probability of the decoder is given. Applying the ideas to a list decoding algorithm by Mahdavifar and Vardy (List-decoding of subspace codes and rank-metric codes up to Singleton bound, ISIT 2012) improves the performance when used as probabilistic unique decoder and gives an upper bound on the failure probability.

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