Variant of the quantum Singleton bound for hybrid stabilizer codes

An $\left[\!\left[n,k\!:\!m,d\!:\!c\right]\!\right]_{q}$ hybrid stabilizer code has length $n$, quantum dimension $k$, classical dimension $m$, quantum minimum distance $d$, and classical minimum distance $c$. Hybrid stabilizer Singleton conjecture. Every such code satisfies

$$k+m\leq n-2\left(d-1\right).$$

This extends the conjectured quantum Singleton bound for arbitrary subsystem codes; the bound is known for $\mathbb{F}_{q}$-linear Clifford subsystem codes, while its validity for general subsystem and hybrid stabilizer codes remains open.