Wiretap encoding of lattices from number fields using codes over Fp

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(ζ_p+ζ_p^-1) using a linear code over F_p. This generalizes the well-known Construction A and provides an efficient coset encoding for algebraic lattices.