The generalized Hamming weight of some BCH codes and related codes

We determine the generalized Hamming weights d_r for 1⩽r⩽h+2 of a binary primitive BCH code with minimum distance d=2 ^h-1. This extends a result of van der Geer and van der Vlugt (see IEEE Trans. on Inform. Theory, vol.40, p. 543-46, 1994 and vol. 41, p.300-1, 1995) who determined d_r, for 1⩽r⩽5 for the triple error correcting primitive BCH code. We also consider the weight hierarchy of some codes with a parity-check polynomial which are the product of two primitive polynomials of the same degree. In particular we have studied some of the codes with few nonzero weights studied by Niho (see Ph.d thesis, University of Southern California, USCEE report 409, Los Angeles, USA)