Documents  16S36 | enregistrements trouvés : 8

- x; 265 p.
ISBN 978-1-4704-1032-2

Contemporary mathematics , 0634

Localisation : Collection 1er étage

anneau non commutatif # théorie des codes # algèbre enveloppante # algèbre des chemins de Leavitt

16N60 ; 16P60 ; 16S34 ; 16S99 ; 16U99 ; 17B35 ; 94B05 ; 94B15 ; 94B60 ; 16-06 ; 16D70 ; 16S36 ; 16D50 ; 00B25

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- VII-270 p.
ISBN 978-0-8218-4771-8

Contemporary mathematics , 0499

Localisation : Collection 1er étage

théorie des groupes # anneaux de groupes # anneau # identité polynomiale # algèbre de Lie # superalgèbre

05A16 ; 16R10 ; 16S36 ; 17B01 ; 17B20 ; 20E08 ; 20C05 ; 20M05 ; 05C05 ; 13F05 ; 16S15 ; 17C10 ; 20E05

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- 436 p.
ISBN 978-0-8218-3630-9

Contemporary mathematics , 0376

Localisation : Collection 1er étage

structure algébrique ordonnée # représentation de graphe # anneau # algèbre de Hopf # algèbre de Artin # algèbre de Hopf tressé # algèbre quantique # anneau de boer # anneau local # code correcteur # fonction de Hilbert # groupe de Coxeter # groupoïde # groupoïde quantique # module # module croisé # module de Verma # paire duale # polynôme orthogonal # quasi-cristal # radical de Jacobson # série discrète de représebtation # trou noir

13D05 ; 13H10 ; 16E10 ; 16G20 ; 16G70 ; 16S36 ; 16W30 ; 94B60

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Research talks

In the 1930’s, in the course of developing non-commutative algebra, Ore introduced a twisted version of polynomials in which the scalars do not commute with the variable. About fifty years later, Delsarte, Roth and Gabidulin realized (independently) that Ore polynomials could be used to define codes—nowadays called Gabidulin codes—exhibiting good properties with respect to the rank distance. More recently, Gabidulin codes have received much attention because of many promising applications to network coding, distributed storage and cryptography.
The first part of my talk will be devoted to review the classical construction of Gabidulin codes and present a recent extension due to Martinez-Penas and Boucher (independently), offering similar performances but allowing for transmitting much longer messages in one shot. I will then revisit Martinez-Penas’ and Boucher’s constructions and give to them a geometric flavour. Based on this, I will derive a geometric description of duals of these codes and finally speculate on the existence of more general geometric Gabidulin codes. In the 1930’s, in the course of developing non-commutative algebra, Ore introduced a twisted version of polynomials in which the scalars do not commute with the variable. About fifty years later, Delsarte, Roth and Gabidulin realized (independently) that Ore polynomials could be used to define codes—nowadays called Gabidulin codes—exhibiting good properties with respect to the rank distance. More recently, Gabidulin codes have received much ...

16S36 ; 94B60

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- 563 p.
ISBN 978-0-582-05947-4

Pitman monographs and surveys in pure and applied mathematics , 053

Localisation : Ouvrage RdC (KARP)

anneau de semigroupe # idéal nilpotent # radical de Jacobson

16N20 ; 16N40 ; 16S36 ; 16W50

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- 500 p.
ISBN 978-0-521-43217-7

Encyclopedia of mathematics and its applications , 0057

Localisation : Collection 1er étage;Réserve

anneau à division # anneaux # application d'extension # construction de corps gauche # coproduit de corps # extension de corps gauche fini # fraction de corps # identité rationnelle # localisation # matrice # relation rationnelle # valuation et ordonnancement des corps gauches # équation et singularité

16S36 ; 16Sxx ; 16U30

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Lecture notes in mathematics , 0123

Localisation : Collection 1er étage

Pli-domaine # anneau d'idéaux gauches principaux # anneau de Goldie gauche # anneau gradué # anneau matriciel # anneau polynômial oblique # anneau quotient gauche # sous-anneau nul # structure de Pli-anneau # théorie d'idéal d'ipli-anneau de Goldie complètement gauche

16P60 ; 16S36 ; 16W50 ; 16W55

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