  Let $L$ be a Moufang loop which is centrally nilpotent of class 2. We first
show that the nuclearly-derived subloop (normal associator subloop) $L^*$ of
$L$ has exponent dividing 6. It follows that $L_p$ (the subloop of $L$ of
elements of $p$-power order) is associative for $p>3$. Next, a loop $L$ is said
to be a {\it small Frattini Moufang loop}, or SFML, if $L$ has a central
subgroup $Z$ of order $p$ such that $C\isom L/Z$ is an elementary abelian
$p$-group. $C$ is thus given the structure of what we call a {\it coded vector
space}, or CVS. (In the associative/group case, CVS's are either orthogonal
spaces, for $p=2$, or symplectic spaces with attached linear forms, for $p>2$.)
Our principal result is that every CVS may be obtained from an SFML in this
way, and two SFML's are isomorphic in a manner preserving the central subgroup
$Z$ if and only if their CVS's are isomorphic up to scalar multiple.
Consequently, we obtain the fact that every SFM 2-loop is a code loop, in the
sense of Griess, and we also obtain a relatively explicit characterization of
isotopy in SFM 3-loops. (This characterization of isotopy is easily extended to
Moufang loops of class 2 and exponent 3.) Finally, we sketch a method for
constructing any finite Moufang loop which is centrally nilpotent of class 2.
