On the Gap between Scalar and Vector Solutions of Generalized Combination Networks

We study scalar-linear and vector-linear solutions to the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a general lower bound on the gap in the alphabet size between scalar-linear and vector-linear solutions.

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