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Roughly speaking, we show that the average $L_\\infty$-distance -- and consequently the $L_1$-distance -- between the weight distribution of a random cosets of $Q$ and the binomial distribution decays quickly as the bilateral minimum distance $d$ of the dual of $Q$ increases. For $d = \\Theta(1)$, it decays like $n^{-\\Theta(d)}$. 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