Auteurs : Pellikaan, Ruud (Auteur de la Conférence)
CIRM (Editeur )
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 :
https://www.cirm-math.fr/RepOrga/1921/Slides/Pellikaan.pdf
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Informations sur la Rencontre
Nom de la rencontre : AGCT - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT - 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
DOI : 10.24350/CIRM.V.19537403
Citer cette vidéo:
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
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Bibliographie
- 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