Strongly Cancellative and Recovering Sets On Lattices

We use information theory to study recovering sets $\R_L$ and strongly cancellative sets $\C_L$ on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in [1], [3] and [5]. We mainly focus on the lattices $B_n$ and $D_{l}^{k}$. Specifically, we find upper bounds and constructions for the sets $\R_{B_n}$, $\C_{B_n}$, and $\C_{D_{l}^{k}}$.