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Suppose X is a uniformly distributed n-dimensional binary vector and Y is obtained by passing X through a binary symmetric channel with crossover probability α. A recent conjecture by Courtade and Kumar postulates that I(f(X);Y)≤ 1-h(α) for any Boolean function f. So far, the best known upper bound was I(f(X);Y)≤ (1-2α)^2. In this paper, we derive a new upper bound that holds for all balanced functions, and improves upon the best known bound for all 13<α<12.arXiv:1505.05794v2 fatcat:ujk2bix7zzd5njkauifx72vwie