A Q-Polymatroid Framework for Information Leakage in Secure Linear Network Coding

We study information leakage in secure linear network coding schemes based on nested rank-metric codes. We show that the amount of information leaked to an adversary that observes a subset of network links is characterized by the conditional rank function of a representable q-polymatroid associated with the underlying rank-metric code pair. Building on this connection, we introduce the notions of q-polymatroid ports and q-access structures and describe their structural properties. Moreover, we extend Massey's correspondence between minimal codewords and minimal access sets to the rank-metric setting and prove a q-analogue of the Brickell–Davenport theorem.