Classes of codes with known generalized Hamming weights and subadditivity properties

Identify broad classes of linear codes C for which the generalized Hamming weights {d_r(C)} are explicitly known; for such classes, determine whether {d_r(C)} and {d_r(C^{⊥})} are subadditive or extended subadditive sequences, and ascertain how the Waldschmidt constants of the Stanley–Reisner ideals I_{Δ(M(C))} and I_{Δ(M(C^{⊥}))} are related.

Background

The paper provides explicit generalized Hamming weight formulas and subadditivity analyses for several families (MDS, constant-weight, first-order affine RM, dual Hamming) and translates these into commutative algebraic invariants via Stanley–Reisner ideals and symbolic powers.

A systematic cataloging of code classes with known generalized Hamming weights, their subadditivity behavior, and the implications for the Waldschmidt constants of I_{Δ(M(C))} and I_{Δ(M(C^{⊥}))} remains open.