  Binary multimedia identifiable parent property codes (binary $t$-MIPPCs) are
used in multimedia fingerprinting schemes where the identification of users
taking part in the averaging collusion attack to illegally redistribute content
is required. In this paper, we first introduce a binary strong multimedia
identifiable parent property code (binary $t$-SMIPPC) whose tracing algorithm
is more efficient than that of a binary $t$-MIPPC. Then a composition
construction for binary $t$-SMIPPCs from $q$-ary $t$-SMIPPCs is provided.
Several infinite series of optimal $q$-ary $t$-SMIPPCs of length $2$ with $t =
2, 3$ are derived from the relationships among $t$-SMIPPCs and other
fingerprinting codes, such as $\overline{t}$-separable codes and $t$-MIPPCs.
Finally, combinatorial properties of $q$-ary $2$-SMIPPCs of length $3$ are
investigated, and optimal $q$-ary $2$-SMIPPCs of length $3$ with $q \equiv 0,
1, 2, 5 \pmod 6$ are constructed.
