  Nuclear modification of the structure function $F_3$ is investigated.
Although it could be estimated in the medium and large $x$ regions from the
nuclear structure function $F_2^A$, it is essentially unknown at small $x$. The
nuclear structure function $F_3^A$ at small $x$ is investigated in two
different theoretical models: a parton-recombination model with $Q^2$ rescaling
and an aligned-jet model. We find that these models predict completely
different behavior at small $x$: {\it antishadowing} in the first parton model
and {\it shadowing} in the aligned-jet model. Therefore, studies of the ratio
$F_3^A/F_3^D$ at small $x$ could be useful in discriminating among different
models, which produce similar shadowing behavior in the structure function
$F_2$. We also estimate currently acceptable nuclear modification of $F_3$ at
small $x$ by using $F_2^A/F_2^D$ experimental data and baryon-number
conservation.
