Linear deterministic broadcast channel

Definition
A linear deterministic broadcast channel is given by a set of channel matrices $\mathbf{H}_i$ each modeling the channel between the source and receiver $i$. Each channel matrix is an $n_i\times m$ matrix over the field $\mathbb{F}_q^{n_i\times m}$. The signal sent from the source is assumed to be an $m$-length vector over the field $\mathbb{F}_q^m$ and thus, the signal received at each receiver is in the form of $y_i=\mathbf{H}_ix$.