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We derive a simple proof, based on information theoretic inequalities, of anupper bound on the largest rates of $q$-ary $\overline{2}$-separable codes thatimproves recent results of Wang for any $q\geq 13$. For the case $q=2$, werecover a result of Lindstr\"om, but with a much simpler derivation. The methodeasily extends to give bounds on $B_2$ codes which, although not improving onWang's results, use much simpler tools and might be useful for futureapplications.

A note on $\overline{2}$-separable codes and $B_2$ codes