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Sur la reconstruction des polynômes linéaires : un nouvel algorithme de décodage des codes de Gabidulin
[On the reconstruction of linearized polynomials: a new decoding algorithm for Gabidulin codes.]
Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 745-750.

We describe a reconstruction problem for linearized polynomials. We equally describe a polynomial-time algorithm enabling to solve this problem in a simple case. From this algorithm we deduce an alternative efficient decoding algorithm for Gabidulin codes introduced in 1985.

Nous présentons un problème de reconstruction de polynômes linéaires ainsi qu'un algorithme en temps polynomial de résolution de ce problème dans un cas simple. Nous en déduisons un algorithme alternatif performant de décodage des codes de Gabidulin introduits en 1985.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.10.004
Pierre Loidreau 1

1 Laboratoire de mathématiques appliquées, ENSTA, 32, bd Victor, 75015 Paris, France
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Pierre Loidreau. Sur la reconstruction des polynômes linéaires : un nouvel algorithme de décodage des codes de Gabidulin. Comptes Rendus. Mathématique, Volume 339 (2004) no. 10, pp. 745-750. doi : 10.1016/j.crma.2004.10.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.004/

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[6] O. Öre On a special class of polynomials, Trans. Amer. Math. Soc., Volume 35 (1933), pp. 559-584

[7] O. Öre Contribution to the theory of finite fields, Trans. Amer. Math. Soc., Volume 36 (1934), pp. 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, Volume 49 (2003) no. 12, pp. 3289-3293

[9] R.M. Roth Maximum-Rank array codes and their application to crisscross error correction, IEEE Trans. Inform. Theory, Volume 37 (1991) no. 2, pp. 328-336

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