MESSAGE RECONSTRUCTION

alice sends different partial messages to a bunch of different receivers. by partial, we mean that one message by itself doesn't convey any meaningful information. let us denote the set of receivers as R. the messages are designed such that if any n receivers get together, they can somehow pool their partial messages together to get a meaningful message -- alice's intended message. however, if any n-1 or less receivers get together, they can't reconstruct anything meaningful whatsoever. n < |R|. what kind of messages are being sent by alice, and what mathematical function do the receivers apply on their pooled partial data to determine the intended message?