We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a ...

We propose new classes of linear codes over integer rings of quadratic extensions of Q, the field of rational numbers. The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a ...

In this paper we describe the quadratic forms over any field k which admit a similarity with a given separable characteristic polynomial f(X) as the transfer of some binary quadratic form associated to the polynomial f(X). ...

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is ...

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is ...

In this paper we present a method for evaluating the center density of algebraic lattices from subfields of Q(xi n), where n is a positive integer. This method allows to reproduce rotated versions of dense lattices in some ...

We use Humbert's reduction theory to introduce an obstruction for the unimodularity of minimal vectors of positive definite quadratic forms over totally real number fields. Using this obstruction we obtain an inequality ...