[On the reconstruction of linearized polynomials: a new decoding algorithm for Gabidulin codes.]
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.
Accepted:
Published online:
Pierre Loidreau 1
@article{CRMATH_2004__339_10_745_0, author = {Pierre Loidreau}, title = {Sur la reconstruction des polyn\^omes lin\'eaires : un nouvel algorithme de d\'ecodage des codes de {Gabidulin}}, journal = {Comptes Rendus. Math\'ematique}, pages = {745--750}, publisher = {Elsevier}, volume = {339}, number = {10}, year = {2004}, doi = {10.1016/j.crma.2004.10.004}, language = {fr}, }
TY - JOUR AU - Pierre Loidreau TI - Sur la reconstruction des polynômes linéaires : un nouvel algorithme de décodage des codes de Gabidulin JO - Comptes Rendus. Mathématique PY - 2004 SP - 745 EP - 750 VL - 339 IS - 10 PB - Elsevier DO - 10.1016/j.crma.2004.10.004 LA - fr ID - CRMATH_2004__339_10_745_0 ER -
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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