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)

On improving 4x4 space-time codes

In this work, we discuss the construction of 4 × 4 space-time codes for coherent MIMO channels. Recently, the so-called perfect space-time codes have been introduced. These are algebraic codes, which satisfy a plethora of properties, that makes them particularly efficient. They are available for 2,3,4 and 6 antennas, and the optimal perfect code for 2 antennas is known. In an attempt to find the optimal perfect code for 4 antennas, we found and present here a (non perfect) code construction that exhibits better performance than 4 × 4 known codes

A Quadratic Form Approach to Construction A of Lattices over Cyclic Algebras

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 give criteria for unimodularity. This yields integral and unimodular lattices with a multiplicative structure. Examples are provided

Invariants cohomologiques des groupes de Coxeter finis

Cette thèse traite des invariants cohomologiques en cohomologie galoisienne des groupes de Coxeter finis en caractéristique nulle. On établit d'abord un principe général d'annulation vérifié par tout invariant cohomologique d'un groupe de Coxeter fini sur un corps de caractéristique nulle suffisamment grand. On utilise ensuite ce principe pour déterminer tous les invariants cohomologiques des groupes de Weyl de type classique à coefficients modulo 2 sur un corps de caractéristique nulle.This PhD thesis deals with cohomological invariants in Galois cohomology of finite Coxeter groups in characteristic zero. We first state a general vanishing principle for the cohomological invariants of a finite Coxeter group over a sufficiently large field of characteristic zero. We then use this principle to determine all the cohomological invariants of the Weyl groups of classical type with coefficients modulo 2 over a field of characteristic zero.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

CM-fields and skew-symmetric matrices

Abstract.: Cohen and Odoni prove that every CM-field can be generated by an eigenvalue of some skew-symmetric matrix with rational coefficients. It is natural to ask for the minimal dimension of such a matrix. They show that every CM-field of degree 2n is generated by an eigenvalue of a skew-symmetric matrix over Q of dimension at most 4n+2. The aim of the present paper is to improve this boun