The BLTA characterization conjecture for decreasing monomial codes

Let $M$ be a decreasing monomial code, let $A\text{-}Aut(M)$ denote its affine automorphism group, and let $BLTA(s,n)$ be the corresponding BLTA group.

BLTA characterization conjecture.

$$BLTA(s,n) = A\text{-}Aut(M)$$

This conjecture concerns the affine automorphisms of decreasing monomial codes, with decreasing polar codes and Reed–Muller codes as special cases. The unrestricted equality $BLTA(s,n)=Aut(M)$ is false in general, since numerical experiments found automorphisms outside BLTA; the affine version is proved in the paper.