Linear Codes, Target Function Classes, and Network Computing Capacity
  We study the use of linear codes for network computing in single-receiver networks with various classes of target functions of the source messages. Such classes include reducible, injective, semi-injective, and linear target functions over finite fields. Computing capacity bounds and achievability are given with respect to these target function classes for network codes that use routing, linear coding, or nonlinear coding. 
Rathinakumar Appuswamy, Massimo Franceschetti, Nikhil Karamchandani,   and Kenneth Zeger
cs.IT cs.DC math.CO math.IT