The coset leader weight enumerator of the code of the twisted cubic | Vidéo | Carmin.tv

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

By Ruud Pellikaan

Appears in collection : Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

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.

Information about the video

Date of recording 11/06/2019
Date of publication 04/07/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19537403
Cite this video Pellikaan, Ruud (11/06/2019). The coset leader weight enumerator of the code of the twisted cubic. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19537403
URL https://dx.doi.org/10.24350/CIRM.V.19537403

Domain(s)

Combinatorics

Bibliography

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

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/1921/Slides/Pellikaan.pdf

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