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 C-1,C-3,C-13 with three zeros alpha, alpha(3), and alpha(13) of length 2(m) - 1 and the weight divisibility of its dual code are studied, where m >= 5 is odd and a is a primitive element of the finite field F-2m. The code C-1,C-3,C-13 is proven to have the same weight distribution as the binary triple-error-correcting primitive BCH code C-1,C-3,C-5 of the same length. (C) 2011 Elsevier Inc. All rights reserved.