  Quantum error-correcting code (QECC) is the central ingredient in
fault-tolerant quantum information processing. An emerging paradigm of
dynamical QECC shows that one can robustly encode logical quantum information
both temporally and spatially in a more resource-efficient manner than
traditional QECCs. Nevertheless, an overarching theory of how dynamical QECCs
achieve fault-tolerance is lacking. In this work, we bridge this gap by
proposing a unified spatio-temporal QECC framework called the ``strategic
code'' built around an ``interrogator'' device which sequentially measures and
evolves the spatial QECC in an adaptive manner based on the ``quantum combs''
formalism, a generalization of the channel-state duality. The strategic code
covers all existing dynamical and static QECC, as well as all physically
plausible QECCs to be discovered in the future, including those that involve
adaptivity in its operational dynamics. Within this framework, we show an
algebraic and an information-theoretic necessary and sufficient
error-correction conditions for a strategic code, which consider spatially and
temporally correlated errors. These conditions include the analogous known
static QECC conditions as a special case. Lastly, we also propose an
optimization-theoretic approach to obtain an approximate strategic code
adapting to a correlated error.
