  We calculate the massive flavor non-singlet Wilson coefficient for the heavy
flavor contributions to the structure function $F_2(x,Q^2)$ in the asymptotic
region $Q^2 \gg m^2$ and the associated operator matrix element $A_{qq,Q}^{(3),
\rm NS}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the
Mellin variable $N$. This matrix element is associated to the vector current
and axial vector current for the even and the odd moments $N$, respectively. We
also calculate the corresponding operator matrix elements for transversity,
compute the contributions to the 3-loop anomalous dimensions to $O(N_F)$ and
compare to results in the literature. The 3-loop matching of the flavor
non-singlet distribution in the variable flavor number scheme is derived. All
results can be expressed in terms of nested harmonic sums in $N$ space and
harmonic polylogarithms in $x$-space. Numerical results are presented for the
non-singlet charm quark contribution to $F_2(x,Q^2)$.
