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Home > Art, Film & Photography > Corps Fini: Code Cyclique, Code Lineaire, Endomorphisme de Frobenius, Conjectures de Weil, Fonction Booleenne, Theoreme de Wedderburn
Corps Fini: Code Cyclique, Code Lineaire, Endomorphisme de Frobenius, Conjectures de Weil, Fonction Booleenne, Theoreme de Wedderburn

Corps Fini: Code Cyclique, Code Lineaire, Endomorphisme de Frobenius, Conjectures de Weil, Fonction Booleenne, Theoreme de Wedderburn


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About the Book

Ce contenu est une compilation d'articles de l'encyclopedie libre Wikipedia. Pages: 29. Non illustre. Chapitres: Code cyclique, Code lineaire, Endomorphisme de Frobenius, Conjectures de Weil, Fonction booleenne, Theoreme de Wedderburn, Analyse harmonique sur un espace vectoriel fini, Code de Reed-Solomon, Algorithme de Berlekamp, Cryptographie sur les courbes elliptiques, Graphe de Paley, Algorithme de Cantor-Zassenhaus, Theoreme de Hasse, Code BCH. Extrait: En mathematiques et plus precisement en algebre, un corps fini est un corps commutatif qui est par ailleurs fini. A isomorphisme pres, un corps fini est entierement determine par son cardinal, qui est toujours une puissance d'un nombre premier, ce nombre premier etant sa caracteristique. Pour tout nombre premier p et tout entier non nul n, il existe un corps de cardinal p, qui se presente comme l'unique extension de degre n du corps premier Z/p Z. Les corps finis sont utilises en theorie algebrique des nombres, ou ils apparaissent comme une structure essentielle a la geometrie arithmetique. Cette branche a permis, entre autres, de demontrer le dernier theoreme de Fermat. Les corps finis ont trouve de nouvelles applications avec le developpement de l'informatique. En theorie des codes, ils permettent par exemple de determiner des codes correcteurs efficaces. Ils interviennent egalement en cryptographie, dans la conception des chiffrements a cle secrete comme le standard AES, ainsi que dans celle des chiffrement a cle publique, a travers, entre autres, le probleme du logarithme discret. Remarque sur la terminologie: la convention la plus courante en francais est de considerer qu'un corps n'est pas necessairement commutatif. Dans le cas des corps finis, la convention est en fait de peu d'importance car, d'apres le theoreme de Wedderburn, tout corps fini est commutatif, et, dans cet article les corps seront supposes d'emblee commutatifs. Les corps finis sont (ou ont ete) appeles egalement corps de Galois, ou pl...


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Product Details
  • ISBN-13: 9781159433963
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Weight: 73 gr
  • ISBN-10: 1159433968
  • Publisher Date: 06 Sep 2011
  • Binding: Paperback
  • Language: French
  • Returnable: N
  • Sub Title: Code Cyclique, Code Lineaire, Endomorphisme de Frobenius, Conjectures de Weil, Fonction Booleenne, Theoreme de Wedderburn
  • Width: 189 mm


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