On the reconstruction of linearized polynomials: A new decoding algorithm for Gabidulin codes;Sur la reconstruction des polynômes linéaires : Un nouvel algorithme de décodage des codes de Gabidulin

Comptes Rendus Mathematique

Volumn 339, Issue 10, 2004, Pages 745-750

  Loidreau, Pierre ^a  

^a ENSTA PARISTECH   (France)

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EID: 8644270555     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2004.10.004     Document Type: Article

References (10)

1. E.R. Berlekamp Algebraic Coding Theory revised 1984 éd. 1984 Aegean Press Park
2. E.R. Berlekamp, L. Welch, Error Correction of Algebraic Block Codes, US Patent, Number 4, 633, 470, 1986
3. E.M. Gabidulin Theory of codes with maximal rank distance Probl. Inf. Transm. 21 1985 1-12
4. E.M. Gabidulin A fast matrix decoding algorithm for rank-error correcting codes In: G. Cohen S. Litsyn A. Lobstein G. Zémor (Eds.) Algebraic Coding in: Lecture Notes in Comput. Sci. 1991 Springer-Verlag 126-133
5. E.M. Gabidulin A.V. Paramonov O.V. Tretjakov Ideals over a non-commutative ring and their application in cryptology in: Lecture Notes in Comput. Sci. vol. 573 1991 482-489
6. O. Öre On a special class of polynomials Trans. Amer. Math. Soc. 35 1933 559-584
7. O. Öre Contribution to the theory of finite fields Trans. Amer. Math. Soc. 36 1934 243-274
8. A.V. Ourivski E.M. Gabidulin B. Honary B. Ammar Reducible rank codes and their applications to cryptography IEEE Trans. Inform. Theory 49 12 2003 3289-3293
9. R.M. Roth Maximum-Rank array codes and their application to crisscross error correction IEEE Trans. Inform. Theory 37 2 1991 328-336
10. M. Sudan Decoding Reed-Solomon codes beyond the error-correction diameter in: Proceedings of the 35th Annual Allerton Conference on Communication, Control and Computing, 29 septembre - 1er octobre 1997 215-224