The binary nonexistence conjecture for self-dual polycyclic codes

A polycyclic code over the binary field $\mathbb{F}_2$ may be self-dual, self-orthogonal, or dual-containing. Binary nonexistence conjecture. There is no self-dual, self-orthogonal, or dual-containing polycyclic code over the binary field. The claim rules out these three duality properties in the binary case; the supplied text gives no evidence of resolution.