Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order.
Etude algorithmique de réseaux construits avec la forme trace. (Algorithmic study of lattices constructed by means of the trace form).
Voisinage au sens de Kneser pour les réseaux quaternioniens.
Designs, groups and lattices
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 -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
Soit un corps de nombres galoisien sur de degré impair, et soit son groupe de Galois. Alors il existe un unique idéal fractionnaire de qui soit unimodulaire pour la forme quadratique . Cet idéal est la racine carrée de la codifférente, et est noté . Dans cet article, on décrit un représentant explicite de la classe de -isométrie du couple , ne dépendant que des nombres premiers sauvagement ramifiés dans , et dont le degré de ramification est différent de .
On extremal additive codes of length to
In this paper we consider the extremal even self-dual -additive codes. We give a complete classification for length . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length and we show that in length such a code is equivalent to the unique -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal -modular lattices.
Odd unimodular lattices of minimum 4
On theta series vanishing at ∞ and related lattices
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