Secrecy-optimality criterion for formally self-dual codes

Let $\code{C}^\ast$ be a formally self-dual code of length $n$. Let $f_{\code{C}}(t)$ be the polynomial associated with a formally self-dual code $\code{C}$, and let $\Gamma_{\mathrm{A}}(\code{C})$ be the corresponding Construction A formally unimodular packing. A code $\code{C}^\ast$ is strongly secrecy-optimal when

$$\code{C}^\ast=\arg\max_{\code{C}\colon\operatorname{formally\ self-dual}}\xi_{\Gamma_{\mathrm{A}}(\code{C})}.$$

Secrecy-optimality criterion. If, for a given formally self-dual code $\code{C}^\ast$ of length $n$,

$$\code{C}^\ast=\arg\min_{\code{C}\colon\operatorname{formally\ self-dual}} f_{\code{C}}\left(\frac{1}{\sqrt{2}}\right),$$

then $\code{C}^\ast$ is strongly secrecy-optimal. This criterion is motivated by the preceding conjecture and the relationship between the secrecy function and the weight-enumerator polynomial. Its validity is not established in the source.