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.
319 Corollary 4.3: For each possible value , there exists a unique additive dual code H of the extended 1-perfect additive non-4-linear code and all these codes H are pairwise nonequivalent, except for = 0 and = 1, where the codes H coincide with the binary dual of the extended Hamming code. ACKNOWLEDGMENT The authors would like to thank the anonymous… (More)
— 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)
Elaborating on a method of Soulé, and using better estimates for the geometry of hermitian lattices, we improve the upper bounds for the torsion part of the K-theory of the rings of integers of number fields.
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.
The aim of this paper is to survey and extend recent results concerning bounds for the Euclidean minima of algebraic number fields. In particular , we give upper bounds for the Euclidean minima of abelian fields of prime power conductor.