The decreasing normalized count conjecture for binary self-dual codes

Let $SD_k$ denote the number of inequivalent binary self-dual codes of dimension $k$, and define

$$a_k=\frac{SD_k(2k)!}{\prod_{i=1}^{k-1}(2^i+1)}.$$

Decreasing normalized count conjecture. The sequence $\{a_k,\ k=10,11,12,\dots\}$ is decreasing. This conjecture concerns the growth of the number of inequivalent binary self-dual codes after normalization by the mass formula. The paper presents it as a conjecture based on the known classifications for dimensions $k\leq 19$; no resolution is given.