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H 1 The coset leader weight enumerator of the code of the twisted cubic

Auteurs : Pellikaan, Ruud (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In general the computation of the weight enumerator of a code is hard and even harder so for the coset leader weight enumerator. Generalized Reed Solomon codes are MDS, so their weight enumerators are known and its formulas depend only on the length and the dimension of the code. The coset leader weight enumerator of an MDS code depends on the geometry of the associated projective system of points. We consider the coset leader weight enumerator of $F_{q}$-ary Generalized Reed Solomon codes of length q + 1 of small dimensions, so its associated projective system is a normal rational curve. For instance in case of the $\left [ q+1,3,q-1 \right ]_{q}$ code where the associated projective system of points consists of the q + 1 points of a plane conic, the answer depends whether the characteristic is odd or even. If the associated projective system of points of a $\left [ q+1,4,q-2 \right ]_{q}$ code consists of the q + 1 points of a twisted cubic, the answer depends on the value of the characteristic modulo 6.

    Keywords : normal rational curve ; twisted cubic ; coset leader weight enumerator

    Codes MSC :
    05B35 - Matroids, geometric lattices
    14H50 - Plane and space curves
    94B05 - Linear codes, general
    94B27 - Geometric methods (including applications of algebraic geometry), See also {11T71}

    Ressources complémentaires :

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/07/2019
      Date de captation : 11/06/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:59:00
      Domaine : Algebra ; Combinatorics ; Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-06-11_Pellikaan.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.19537403
    Cite this video as: Pellikaan, Ruud (2019). The coset leader weight enumerator of the code of the twisted cubic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19537403
    URI : http://dx.doi.org/10.24350/CIRM.V.19537403

    Voir aussi


    1. Jurrius, R. P. M. J., & Pellikaan, G. R. (2009). The extended coset leader weight enumerator. In Proceedings 30th Symposium on Information Theory on the Benelux (Eindhoven, The Netherlands, May 28-29, 2009) (pp. 217-224). Technische Universiteit Eindhoven. - https://www.relindejurrius.nl/publications/2009_WIC.pdf

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