  We propose a lattice construction from totally real and CM fields, which
naturally generalizes the Construction A of lattices from $p$-ary codes
obtained from the cyclotomic field $\mathbb{Q}(\zeta_p)$, $p$ 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
$\mathbb{Q}(\zeta_{p^r}+\zeta_{p}^{-r})$ of the cyclotomic field
$\mathbb{Q}(\zeta_{p^r})$, $r\geq 1$. Our construction has applications to
coset encoding of algebraic lattice codes, and we detail the case of coset
encoding of block fading wiretap codes.
