On generalized Hamming weights of binary primitive BCH codes with minimum distance one less than a power of two

The generalized Hamming weights introduced by Wei (1991) have been shown to be fundamental descriptive parameters of a linear block code. They have been found to be useful in certain cryptographic applications and in the studies of minimal trellis diagrams of linear block codes. In this correspondence, we determine the first few and the last few generalized Hamming weights of binary primitive BCH codes with minimum distance one less than a power of two, of their extensions, and of the duals of both