Fast decoding of Gabidulin codes

DOI10.1007/s10623-012-9659-5zbMath1259.94082OpenAlexW2049833502MaRDI QIDQ1934220

Valentin Afanassiev, Antonia Wachter-Zeh, Vladimir Sidorenko

Publication date: 28 January 2013

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00614474/file/13.pdf

zbMATH Keywords

Gabidulin codeslinearized polynomialsrank metricfast decodingfast symbolic divisionfast symbolic product

Mathematics Subject Classification ID

Decoding (94B35)

Related Items (17)

On the list decodability of rank-metric codes containing Gabidulin codes ⋮ Fast operations on linearized polynomials and their applications in coding theory ⋮ Unnamed Item ⋮ Covering Radius of Matrix Codes Endowed with the Rank Metric ⋮ On transform-domain error and erasure correction by Gabidulin codes ⋮ Fast decoding of Gabidulin codes ⋮ Concatenation of convolutional codes and rank metric codes for multi-shot network coding ⋮ Extension of Overbeck's attack for Gabidulin-based cryptosystems ⋮ A new McEliece-type cryptosystem using Gabidulin-Kronecker product codes ⋮ Fast skew-feedback shift-register synthesis ⋮ On decoding additive generalized twisted Gabidulin codes ⋮ Partition-balanced families of codes and asymptotic enumeration in coding theory ⋮ Systematic encoders for generalized Gabidulin codes and the \(q\)-analogue of Cauchy matrices ⋮ Extending Coggia-Couvreur attack on Loidreau's rank-metric cryptosystem ⋮ Dynamics of the \(a\)-map over residually finite Dedekind domains and applications ⋮ New rank codes based encryption scheme using partial circulant matrices ⋮ Rank-Metric Codes and Their Applications

Cites Work

• Probabilistic algorithm for finding roots of linearized polynomials
• Theory of codes with maximum rank distance
• Bilinear forms over a finite field, with applications to coding theory
• Theory of non-commutative polynomials
• Fast decoding of Gabidulin codes
• Coding for Errors and Erasures in Random Network Coding
• A Rank-Metric Approach to Error Control in Random Network Coding
• A method for solving key equation for decoding goppa codes
• Linearized Shift-Register Synthesis
• Maximum-rank array codes and their application to crisscross error correction
• Coding and Cryptography
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