Grégory Berhuy

On the Existence of Perfect Space–Time Codes

Perfect space-time codes are codes for the coherent multiple-input multiple-output (MIMO) channel. They have been called so since they satisfy a large number of design criteria that makes their performances outmatch many other codes. In this correspondence, we discuss the existence of such codes (or more precisely, the existence of perfect codes with optimal signal complexity).

An introduction to Galois cohomology and its applications

Foreword Jean-Pierre Tignol Introduction Part I. An Introduction to Galois Cohomology: 1. Infinite Galois theory 2. Cohomology of profinite groups 3. Galois cohomology 4. Galois cohomology of quadratic forms 5. Etale and Galois algebras 6. Groups extensions and Galois embedding problems Part II. Applications: 7. Galois embedding problems and the trace form 8. Galois cohomology of central simple algebras 9. Digression: a geometric interpretation of H1 (-, G) 10. Galois cohomology and Noethers problem 11. The rationality problem for adjoint algebraic groups 12. Essential dimension of functors References Index.

Space-time codes from crossed product algebras of degree 4

We study crossed product algebras of degree 4, and present a new space-time code construction based on a particular crossed product division algebra which exhibits very good performance.

On hermitian trace forms over hilbertian fields

Abstract. Let k be a field of characteristic different from 2. Let

On Improving 4 × 4 Space-Time Codes

E/k

Algebraic space-time codes based on division algebras with a unitary involution

be a finite separable extension with a {\it k}-linear involution

ON THE COMPUTATION OF TRACE FORMS OF ALGEBRAS WITH INVOLUTION

\sigma

Essential dimension : a functorial point of view (after A. Merkurjev)

. For every

On the notion of canonical dimension for algebraic groups

\sigma

Galois cohomology of the classical groups over imperfect fields

-symmetric element