3 papers
cs.IT2020
A Quadratic Form Approach to Construction A of Lattices over Cyclic Algebras
Grégory Berhuy, Frédérique Oggier
We propose a construction of lattices from (skew-) polynomial codes, by endowing quotients of some ideals in both number fields and cyclic algebras with a suitable trace form. We g…
cs.IT2019
Rank weights for arbitrary finite field extensions
Grégory Berhuy, Jean Fasel, Odile Garotta
In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known…
math.AG2004
On the notion of canonical dimension for algebraic groups
G. Berhuy, Z. Reichstein
We define and study a new numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the…