Constructions of t-strongly multimedia IPP codes with length \(t+1\)

Strongly multimedia identifiable parent property code (t-SMIPPC) was introduced for protecting multimedia contents from illegally redistributing under the averaging collusion attack. Such a code has efficient algorithms for tracing colluders. However, there are few results about the existence of such codes up to now. In this paper, we focus on t-SMIPPCs with length \(t+1\) $t+1$ where \(t \ge 2\) $t\ge 2$ is an integer. We first improve the lower bound on the size of such codes. For the case \(t=2\) $t=2$ , i.e., 2-SMIPPCs with length 3, we further investigate combinatorial properties of the codes. Based on these properties, optimal q-ary 2-SMIPPCs with length 3 are constructed for \(q\equiv 0,1,2,5 \pmod 6\) $q\equiv 0,1,2,5(mod6)$ .