Derive a Griesmer-type bound for generalized Hamming weights of additive codes

Derive a Griesmer-type bound for the fth generalized Hamming weight of additive codes in the cases h,f\ge 2, equivalently, for the parameters n_q(r,h,f;s) with both the subspace dimension parameter h and codimension parameter f at least two.

Background

For linear codes, the paper recalls a Griesmer-type bound for generalized Hamming weights, and for additive codes with f=1 it cites results that determine n_q(r,h,1;s) for sufficiently large s.

The corresponding bound for additive codes involving generalized Hamming weights with h,f\ge 2 is not known. Such a result would extend the Griesmer-bound framework from linear and ordinary additive-code settings to the paper’s more general geometric systems.