NDLI: Fast decoding of Gabidulin codes

Content Provider	Springer Nature Link
Author	Wachter Zeh, Antonia Sidorenko, Vladimir Afanassiev, Valentin
Copyright Year	2012
Abstract	Gabidulin codes are the analogues of Reed–Solomon codes in rank metric and play an important role in various applications. In this contribution, a method for efficient decoding of Gabidulin codes up to their error correcting capability is shown. The new decoding algorithm for Gabidulin codes (defined over $${\mathbb{F}_{q^m}}$$ ) directly provides the evaluation polynomial of the transmitted codeword. This approach can be seen as a Gao-like algorithm and uses an equivalent of the Euclidean Algorithm. In order to achieve low complexity, a fast symbolic product and a fast symbolic division are presented. The complexity of the whole decoding algorithm for Gabidulin codes is $${\mathcal{O} (m^3 \, \log \, m)}$$ operations over the ground field $${\mathbb{F}_q}$$ .
Ending Page	73
Page Count	17
Starting Page	57
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	1-3
Volume Number	66
Language	English
Publisher	Springer US
Publisher Date	2012-04-04
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Fast symbolic product Information and Communication, Circuits Rank metric Data Encryption Fast symbolic division Decoding Data Structures, Cryptology and Information Theory Fast decoding Discrete Mathematics in Computer Science Linearized polynomials Coding and Information Theory Gabidulin codes Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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