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Motivated by recent work on entanglement-assisted codes for sending messages over classical channels, the larger, easily characterized class of nonsignaling codes is defined. Analyzing the optimal performance of these codes yields an alternative proof of the finite block length converse of Polyanskiy, Poor, and Verdú, and shows that they achieve this converse. This provides an explicit formulation of the converse as a linear program which has some useful features. For discrete memoryless channels, it is shown that nonsignaling codes attain the channel capacity with zero error probability if and only if the dispersion of the channel is zero.