Automorphism-group PD-set conjecture for one-point AG codes

Let $C$ be a one-point algebraic-geometric code associated to the curve

$$y^2=x^p-x$$

over $GF(p^2)$, with length $n=2p(p-1)+p$, and let $X$ be the corresponding curve over a field $F$. Arrange the points in $X(F)$ suitably, and let $Aut_F(X)$ denote the automorphism group of $X$ over $F$. A permutation decoding set (PD-set) is a set of coordinate permutations that moves every correctable error pattern out of the information positions. The automorphism-group PD-set conjecture. Permutation decoding always applies and is more computationally efficient than the standard decoding algorithm. If the points in $X(F)$ are arranged suitably, the image of $Aut_F(X)$ in the permutation group of $C$ may be used as a PD-set. Its complexity is at most the size of the automorphism group of $X$, which should be

$$O(p^2)=O(g^2)=O(n).$$

This proposes using geometric automorphisms to construct permutation-decoding sets and predicts a complexity improvement over standard decoding; the source gives no resolution of the conjecture.