2026/07/29 by Eric Kubischta, Ian Teixeira
Computer Science · Mathematics · Physics and Astronomy · #cs.IT #math.IT #quant-ph
arxiv created 2026/07/29 · arxiv updated 2026/07/30
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.