On $2$-parent-identifying set systems of block size $4$

Abstract

Parent-identifying set system is a kind of combinatorial structures with applications to broadcast encryption. In this paper we investigate the maximum number of blocks $I_2(n,4)$ in a $2$-parent-identifying set system with ground set size $n$ and block size $4$. The previous best known lower bound states that $I_2(n,4)=\Omega (n^{4/3+o(1)})$. We improve this lower bound by showing that $I_2(n,4)=\Omega (n^{3/2-o(1)})$ using techniques in additive number theory.

11 pages, A section for discussion on IPP set systems and IPP codes were added, together with related references