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We derive a simple proof, based on information theoretic inequalities, of an upper bound on the largest rates of q -ary 2 ‾ -separable codes that improves recent results of Wang for any q ≥ 13. For the case q = 2 , we recover a result of Lindström, but with a much simpler derivation. The method easily extends to give bounds on B 2 codes which, although not improving on Wang's results, use much simpler tools and might be useful for future applications. [ABSTRACT FROM AUTHOR]