On the fan associated to a linear code

Natalia Dück (1) , Irene Márquez-Corbella (2, 3) , Edgar Martínez-Moro (4)

1 Hamburg University of Technology
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 GRACE - Geometry, arithmetic, algorithms, codes and encryption
4 Department of Applied Mathematics, University of Valladolid,

We will show how one can compute all reduced Gröbner bases with re-spect to a degree compatible ordering for code ideals -even though these binomial ideals are not toric. To this end, the correspondence of linear codes and binomial ideals will be briefly described as well as their resemblance to toric ideals. Finally, we will hint at applications of the degree compatible Gröbner fan to the code equivalence problem.

Mots clés: Linear code; Gröbner basis; Gröbner fan

Domaines: Géométrie algébrique [math.AG]; Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Natalia Dück, Irene Márquez-Corbella, Edgar Martínez-Moro. On the fan associated to a linear code . 4th ICMCTA - Fourth International Castle Meeting on Coding Theory and Applications, Sep 2014, Palmela, Portugal. ⟨hal-01088432⟩