  The binary primitive triple-error-correcting BCH code is a cyclic code of
minimum distance 7 with generator polynomial having zeros $\alpha$, $\alpha^3$
and $\alpha^5$ where $\alpha$ is a primitive root of unity. The zero set of the
code is said to be {1,3,5}. In the 1970's Kasami showed that one can construct
similar triple-error-correcting codes using zero sets consisting of different
triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new
triples leading to triple-error-correcting codes. In this paper a new such
triple is presented. In addition a new method is presented that may be of
interest in finding further such triples.
