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H 1 Ore polynomials and application to coding theory

Auteurs : Caruso, Xavier (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : 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.

    Keywords : noncommutative polynomials; coding theory; rank metric

    Codes MSC :
    16S36 - Ordinary and skew polynomial rings and semigroup rings, See also {20M25}
    94B60 - Other types of codes

    Ressources complémentaires :

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/07/2019
      Date de captation : 13/06/2019
      Sous collection : Research talks
      Format : MP4
      arXiv category : Rings and Algebras ; Symbolic Computation
      Domaine : Algebraic & Complex Geometry ; Algebra
      Durée : 00:57:58
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-06-13_Caruso.mp4

    Informations sur la rencontre

    Nom de la rencontre : Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisateurs de la rencontre : Ballet, Stéphane ; Bisson, Gaetan ; Bouw, Irene
    Dates : 10/06/2019 - 14/06/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1921.html

    Citation Data

    DOI : 10.24350/CIRM.V.19537603
    Cite this video as: Caruso, Xavier (2019). Ore polynomials and application to coding theory. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19537603
    URI : http://dx.doi.org/10.24350/CIRM.V.19537603

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