Designs, groups and lattices

Christine Bachoc[1]

  • [1] Université Bordeaux I 351, cours de la Libération 33405 Talence, France

Journal de Théorie des Nombres de Bordeaux (2005)

  • Volume: 17, Issue: 1, page 25-44
  • ISSN: 1246-7405

Abstract

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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.

How to cite

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Bachoc, Christine. "Designs, groups and lattices." Journal de Théorie des Nombres de Bordeaux 17.1 (2005): 25-44. <http://eudml.org/doc/249471>.

@article{Bachoc2005,
abstract = {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.},
affiliation = {Université Bordeaux I 351, cours de la Libération 33405 Talence, France},
author = {Bachoc, Christine},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Grassmannian spaces; Grassmannian design; Clifford group},
language = {eng},
number = {1},
pages = {25-44},
publisher = {Université Bordeaux 1},
title = {Designs, groups and lattices},
url = {http://eudml.org/doc/249471},
volume = {17},
year = {2005},
}

TY - JOUR
AU - Bachoc, Christine
TI - Designs, groups and lattices
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2005
PB - Université Bordeaux 1
VL - 17
IS - 1
SP - 25
EP - 44
AB - 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 - eng
KW - Grassmannian spaces; Grassmannian design; Clifford group
UR - http://eudml.org/doc/249471
ER -

References

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