Subadditivity of generalized Hamming weights for higher-order affine Reed–Muller codes and their duals

Investigate whether, for affine Reed–Muller codes RM_q(a,m) of order a>1 over a finite field F_q, the generalized Hamming weights {d_r(RM_q(a,m))} and the generalized Hamming weights of their dual codes {d_r(RM_q(a,m)^{⊥})} form subadditive or extended subadditive sequences.

Background

For first-order affine Reed–Muller codes RM_q(1,m), the paper proves that the generalized Hamming weights form an extended subadditive sequence and derives exact formulas for α(I_Δ^{(s)}) and the Waldschmidt constant.

For higher-order RM_q(a,m) with a>1, closed formulas for generalized Hamming weights can be far more involved, and the paper does not establish subadditivity properties, raising this question for both the codes and their duals.