Construction A of Lattices Over Number Fields and Block Fading (Wiretap) Coding

We propose a lattice construction from totally real and complex multiplication fields, which naturally generalizes Construction A of lattices from p-ary codes obtained from the cyclotomic field Q(ζ_p), p a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield Q(ζ_p^r + ζ_p^-r ) of the cyclotomic field Q(ζ_p^r ), r ≥ 1. Our construction has applications to coset encoding of algebraic lattice codes for block fading channels, and in particular for block fading wiretap channels.