A construction of laminated lattices of full diversity in odd dimensions $d$ with $3\le d\le 15$ is presented. The technique, which uses a combination of number fields and error-correcting codes, consists essentially of two steps: In the first, the Abelian number field $F$ of degree $d$ and prime conductor $p$, where $p$ is a prime congruent to 1 modulo $d$, is considered. In the second, the lattice is obtained as the canonical embedding (Minkowski homomorphism) of a $\mathbb{Z}$-submodule of ${\mathfrak{𝔒}}_F$, the ring of integers of $F$. The submodule is defined by the parity-check matrices of a Reed–Solomon code over $GF\left(p\right)$ and a suitably chosen linear code, typically either binary or over $\mathbb{Z}∕4\mathbb{Z}$, the ring of integers modulo 4.