The trinomial constructions of iso-dual polycyclic codes

Let $q$ be a prime power and consider the indicated trinomial-associated polycyclic codes. Iso-dual construction conjecture. The following codes are isodual:

• If $q$ is a power of an odd prime, a code associated with $x^{2m}\pm 2cx^m+c^2$ and generated by $g(x)=\pm x^m\pm c$.
• If $q$ is a power of $2$, a code associated with $x^{2m}+a^2x^{2i}+b^2$ and generated by $g(x)=x^m+ax^i+b$.

These are proposed on the basis of preceding results and computational evidence; the source does not provide a resolution of the conjectured constructions.