  Quantum error correction (QEC) codes protect quantum information from errors
due to decoherence. Many of them also serve as prototypical models for exotic
topological quantum matters. Investigating the behavior of the QEC codes under
decoherence sheds light on not only the codes' robustness against errors but
also new out-of-equilibrium quantum phases driven by decoherence. The phase
transitions, including the error threshold, of the decohered QEC codes can be
probed by the systems' R\'enyi entropies $S_R$ with different R\'enyi indices
$R$. In this paper, we study the general construction of the statistical models
that characterize the R\'enyi entropies of QEC codes decohered by Pauli noise.
We show that these statistical models can be organized into a "tapestry" woven
by rich duality relations among them. For Calderbank-Shor-Steane (CSS) codes
with bit-flip and phase-flip errors, we show that each R\'enyi entropy is
captured by a pair of dual statistical models with randomness. For
$R=2,3,\infty$, there are additional dualities that map between the two error
types, relating the critical bit-flip and phase-flip error rates of the
decoherence-induced phase transitions in the CSS codes. For CSS codes with an
"$em$ symmetry" between the $X$-type and the $Z$-type stabilizers, the
dualities with $R=2,3,\infty$ become self-dualities with super-universal
self-dual error rates. These self-dualities strongly constrain the phase
transitions of the code signaled by $S_{R=2,3,\infty}$. For general stabilizer
codes decohered by generic Pauli noise, we also construct the statistical
models that characterize the systems' entropies and obtain general duality
relations between Pauli noise with different error rates.
