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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)
The notion of Euclidean minimum of a number field is a classical one. In this paper we generalize it to central division algebras and establish some general results in this new context.
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 negligeable coding gain. Lattice constellations with high… (More)
For a number field F , it is proved that the K2-semigroup K2(F,F++) defined in [R.V. Moody, J. Morita, J. Algebra 229 (2000) 1] has similar properties to the positive K2 group K + 2 (F) introduced by Gras in [J. Number Theory 23 (1986) 322]. 2003 Elsevier Inc. All rights reserved.
Let k be a field of characteristic different from 2 and let G be a finite group. A G-form over k is a G-invariant quadratic form defined over k. An important class of G-forms consists of the trace forms qL associated to G-Galois algebras L. Here a G-Galois algebra is a finite étale k-algebra that is Galois over k with group G. See Section 1 and [8, 1.3] for… (More)
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear formswithout any symmetry property. The present paperwill establish aWitt cancellation result, an analogue of Springer’s theorem, as well as some local–global and finiteness results in… (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 pr , where p is an odd prime number and r ≥ 2.