Generalized $M_{m,r}$ -Network: A Case for Fixed Message Dimensions

In this letter, we first present a class of networks named null Generalized null null null null {{M}}_{{ \textit {m, r}}}null null null -Network null for every integer null null null {m} \geq 2null null null and null null null \forall {r} \in \{0, 1,\ldots, {m}-1\}null null null and we show that every network of this class admits a vector linear solution if and only if the message dimension is an integer multiple of null null null {m}..