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 -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 -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.
@article{JTNB_2005__17_1_25_0,
author = {Christine Bachoc},
title = {Designs, groups and lattices},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {25--44},
publisher = {Universit\'e Bordeaux 1},
volume = {17},
number = {1},
year = {2005},
doi = {10.5802/jtnb.474},
zbl = {1074.05023},
mrnumber = {2152208},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.474/}
}
TY - JOUR TI - Designs, groups and lattices JO - Journal de Théorie des Nombres de Bordeaux PY - 2005 DA - 2005/// SP - 25 EP - 44 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.474/ UR - https://zbmath.org/?q=an%3A1074.05023 UR - https://www.ams.org/mathscinet-getitem?mr=2152208 UR - https://doi.org/10.5802/jtnb.474 DO - 10.5802/jtnb.474 LA - en ID - JTNB_2005__17_1_25_0 ER -
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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