Some results on the minimum weight of primitive BCH codes (Corresp.)

For
1 \leq i \leq m - s- 2
and
0 \leq s \leq m -2i
, the intersection of the binary BCH code of designed distance
2 ^{m-s-1} - 2 ^{m-s-t-1} - 1
and length
2^m - 1
with the shortened
(s + 2)
th-order Reed-Muller code of length
2^m -- 1
has codewords of weight
2^{m-s-1} - 2^{m-s-t-1} - 1
.