Classical and Quantum MacWilliams Transforms as Spin Kinematics

Eric Kubischta; Ian Teixeira

Classical and Quantum MacWilliams Transforms as Spin Kinematics

量子物理 2026-07-29 v1 信息论

作者: Eric Kubischta , Ian Teixeira

摘要

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- $D$ rotation between two canonical bases. Within each classical and quantum theory, changing the length $n$ leaves the rotation untouched: the same element simply reappears at spin $n/2$ . And at fixed $n$ , changing the rotation axis simply moves between the various classical and quantum theories.

引用

@article{arxiv.2607.27173,
  title  = {Classical and Quantum MacWilliams Transforms as Spin Kinematics},
  author = {Eric Kubischta and Ian Teixeira},
  journal= {arXiv preprint arXiv:2607.27173},
  year   = {2026}
}