Subadditivity of generalized Hamming weights for projective Reed–Muller codes

Determine whether the generalized Hamming weights of projective Reed–Muller codes PRM_q(a,m) form subadditive or extended subadditive sequences.

Background

The paper establishes extended subadditivity for the generalized Hamming weights of the dual binary Hamming code (a projective Reed–Muller code of order one) but notes that generalized Hamming weights for general projective Reed–Muller codes are largely unknown.

This motivates asking whether similar subadditivity or extended subadditivity properties hold in the broader projective Reed–Muller family.