Encodes \(K\)-dimensional Hilbert space into a \(q^n\)-dimensional (\(n\)-qudit) Hilbert space, where the canonical qudit basis consists of states of a quantum mechanical spin. In other words, canonical single-qudit states \(|^\ell_m\rangle\) are labeled by total angular momentum \(\ell\) (either integer or half-integer) and its \(z\)-axis projection \(m\), with \(q=2\ell+1\).
In contrast to other qudit codes, spin codes are closely associated with the angular momentum Lie algebra and/or the Lie groups \(SU(2)\) or \(SO(3)\).
“Spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spins_into_spins