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Designs, groups and lattices

Christine Bachoc — 2005

Journal de Théorie des Nombres de Bordeaux

The notion of designs in Grassmannian spaces was introduced by the author and R. Coulangeon, G. Nebe, in []. After having recalled some basic properties of these objects and the connections with the theory of lattices, we prove that the sequence of Barnes-Wall lattices hold 6 -Grassmannian designs. We also discuss the connections between the notion of Grassmannian design and the notion of design associated with the symmetric space of the totally isotropic subspaces in a binary quadratic space, which...

Sur la structure hermitienne de la racine carrée de la codifférente

Christine Bachoc — 1993

Annales de l'institut Fourier

Soit K un corps de nombres galoisien sur ℚ de degré impair, et soit G son groupe de Galois. Alors il existe un unique idéal fractionnaire de K qui soit unimodulaire pour la forme quadratique Trace K / ℚ ( x 2 ) . Cet idéal est la racine carrée de la codifférente, et est noté A K . Dans cet article, on décrit un représentant explicite de la classe de ℤ [ G ] -isométrie du couple ( A K , Trace K / ℚ ( x 2 ) ) , ne dépendant que des nombres premiers p sauvagement ramifiés dans K , et dont le degré de ramification est différent de p .

On extremal additive 𝔽 4 codes of length 10 to 18

Christine Bachoc;  Philippe Gaborit — 2000

Journal de théorie des nombres de Bordeaux

In this paper we consider the extremal even self-dual 𝔽 4 -additive codes. We give a complete classification for length 10 . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length 14 and we show that in length 18 such a code is equivalent to the unique 𝔽 4 -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal 3 -modular lattices.

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