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 their minimum product distance using the corresponding properties.

Let \alpha be a Salem number of degree d with 4 \leqslant 18 . We show that if \equiv 0, \ {\rm or}\ 6 \allowbreak{\rm (mod 8)} , then is the dynamical an automorphism complex (non-projective) K3 surface. define notion signature automorphism, and use it to give criterion for numbers 10 realized as such automorphism. The first part paper contains results on isometries lattices.

In this work, we give a bound on performance of any full-diversity lattice constellation constructed from algebraic number fields. We show that most the already available constructions are almost optimal in sense further improvement minimum product distance would lead to negligible coding gain. Furthermore, discuss constructions, distance, and bounds for complex rotated Z[i]/sup n/-lattices dimension n, which avoid need component interleaving.

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally cyclotomic prime power discriminant.

We give necessary and sufficient conditions for an orthogonal group defined over a global field of characteristic ≠2 to contain maximal torus given type.

Let k be a global field of characteristic not 2, and let f \in k[X] an irreducible polynomial. We show that non-degenerate quadratic space has isometry with minimal polynomial if only such exists over all the completions . This gives partial answer to question Milnor.

We give necessary and sufficient conditions for an integral polynomial without linear factors to be the characteristic of isometry some even, unimodular lattice given signature. This gives rise Hasse principle questions, which we answer in a more general setting. As application, prove signatures knots.

We prove that the category of systems sesquilinear forms over a given hermitian is equivalent to unimodular 1-hermitian another category. The are not required be or defined on reflexive object (i.e. standard map from its double dual assumed bijective), and in system can with respect different structures This extends result obtained by E. Bayer-Fluckiger D. Moldovan. use equivalence define Witt ring category, also generalize various results (e.g.: Witt's Cancelation Theorem, Springer's weak...

The notion of Euclidean minimum a number field is classical one. In this paper, we generalize it to central division algebras and establish some general results in new context.