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General methods from  are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.
In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a negligible coding gain. Furthermore, we discuss constructions,… (More)
In this correspondence, we present various families of full diversity rotated Z/sup n/-lattice constellations based on algebraic number theory constructions. We are able to give closed-form expressions of their minimum product distance using the corresponding algebraic properties.
— In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most of the already available constructions are almost optimal in the sense that any further improvement of the minimum product distance would lead to a neg-ligeable coding gain. Lattice constellations with high… (More)
The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor p r , where p is an odd prime number and r ≥ 2.
Let G be a finite group and let k be a field of char(k) = 2. We explicitly describe the set of trace forms of G-Galois algebras over k when the virtual 2-cohomological dimension vcd 2 (k) of k is at most 1. For fields with vcd 2 (k) ≤ 2 we give a cohomological criterion for the orthogonal sum of a trace form of a G-Galois algebra with itself to be… (More)
Aims and Scope Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal is intended for the publication of original research articles on all aspects in mathematics.
In this paper we define a notion of Witt group for sesquilinear forms in hermitian categories, which in turn provides a notion of Witt group for sesquilin-ear forms over rings with involution. We also study the extension of scalars for K-linear hermitian categories, where K is a field of characteristic = 2. We finally extend several results concerning… (More)