Classical and Quantum MacWilliams Transforms as Spin Kinematics
arXiv:2607.27173
The paper shows that MacWilliams transforms for both classical and quantum error‑correcting codes can be derived as spin‑kinematic operations, specifically as Wigner‑D rotations between canonical bases, with the same rotation applying uniformly across code lengths.
Abstract
Spin is the hidden engine behind the zoo of MacWilliams transforms in weight enumerator theories - not only for qubits and qudits, but even for classical codes. From nothing more than a split into trivial and nontrivial errors, we kinematically derive the MacWilliams transform as a Wigner- rotation between two canonical bases. Within each classical and quantum theory, changing the length leaves the rotation untouched: the same element simply reappears at spin . And at fixed , changing the rotation axis simply moves between the various classical and quantum theories.