The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)

Let
r_{i}
be the covering radius of the
(2^{i},i+ 1)
Reed-Muller code. It is an open question whether
r_{2m+1}=2^{2_{m}}-2m
holds for all
m
. It is known to be true for
m=0,1,2
, and here it is shown to be also true for
m=3
.