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(ζp), 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(ζpr+ ζp-r) of the cyclotomic field Q(ζpr), 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.

We consider the problem of communication over a block fading wiretap channel. It is known that coding for such a channel can be done using nested lattice codes constructed over totally real number fields. In this paper, we propose a method for encoding an integral lattice over the ring of integers of a totally real number field, and study in particular the case of Q(ζp+ζp-1) using a linear code over Fp. This generalizes the well-known Construction A and provides an efficient coset encoding for algebraic lattices.