All binary 3-error-correcting BCH codes of length2^m-ihave covering radius 5 (Corresp.)

Van der Horst and Berger have conjectured that the covering radius of the binary 3-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length
2^{m} - l, m \geq 4
is 5. Their conjecture was proved earlier when
m \equiv 0, 1
, or 3 (mod 4). Their conjecture is proved when
m \equiv 2
(mod 4).