A map f : V := GF(2(m)) -> V is APN (almost perfect nonlinear) if its directional derivatives in nonzero directions are all 2-to-1. If m is greater than 2 and f vanishes at 0, then this derivative condition is equivalent to the condition that the binary linear code of length 2(m) - 1, whose parity check matrix has jth column equal to [f((omega j))(omega j)], is double-error-correcting, where. is primitive in V. Carlet et al. (Designs Codes Cryptogr 15: 125-156, 1998) proved that this code has dimension 2(m) - 1 - 2m; but their indirect proof uses a subtle argument involving general code parameter bounds to show that a double-error correcting code of this length could not be larger. We show here that this result follows immediately from a well-known result on bent functions ... a subject dear to the heart of Jacques Wolfmann.
