  We investigate orbifold constructions of conformal field theories from
lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$,
concentrating on the case $p=3$. Explicit expressions are given for most of the
relevant vertex operators, and we consider the locality relations necessary for
these to define a consistent conformal field theory. A relation to
constructions of lattices from codes, analogous to that found in earlier work
in the $p=2$ case which led to a generalisation of the triality structure of
the Monster module, is also demonstrated.
