A non-cyclic triple-error-correcting BCH-like code and some minimum distance results

In this paper, we give the first example of a non-cyclic triple-error-correcting code which is not equivalent to the primitive BCH code. It has parameters [63, 45, 7]. We also give better bounds on minimum distances of some [2 n − 1, 2 n - 3 n - 1] cyclic codes with three small zeroes. Finally, we reprove weight distribution results of Kasami for triple-error-correcting BCH-like codes using direct methods.