A triple-error-correcting cyclic code from the Gold and Kasami–Welch APN power functions

Based on a sufficient condition proposed by Hollmann and Xiang for constructing triple-error-correcting codes, the minimum distance of a binary cyclic code C1,3,13 with three zeros α, α3, and α13 of length m2−1 and the weight divisibility of its dual code are studied, where m⩾5 is odd and α is a primitive element of the finite field Fm2. The code C1,3,13 is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code C1,3,5 of the same length.