In this paper "Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures" on page 286 it's written "The independence of the mappings $\lbrace \phi _j \rbrace _{j \in H_G}$, implies that $ker\varphi _h^0 + (\cap _{j \in H_G} ker \varphi _j^0 )=E_0^l$." May I ask for more explanation of this sentence please?
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