Designs, groups and lattices
Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 25-44.

The notion of designs in Grassmannian spaces was introduced by the author and R. Coulangeon, G. Nebe, in [3]. 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 is revealed in a certain construction involving the Clifford group.

La notion de designs dans les espaces Grassmanniens a été introduite par l’auteur et R. Coulangeon, G. Nebe dans [3]. Après avoir rappelé les premières propriétés de ces objets et les relations avec la théorie des réseaux, nous montrons que la famille des réseaux de Barnes-Wall contient des 6-designs grassmanniens. Nous discutons également des relations entre cette notion de designs et les designs associés à l’espace symétrique formé des espaces totalement isotropes d’un espace quadratique binaire, qui sont mises en évidence par une certaine construction utilisant le groupe de Clifford.

Published online:
DOI: 10.5802/jtnb.474
Christine Bachoc 1

1 Université Bordeaux I 351, cours de la Libération 33405 Talence, France
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Christine Bachoc. Designs, groups and lattices. Journal de Théorie des Nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 25-44. doi : 10.5802/jtnb.474. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.474/

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