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In quantum information, the gnu code refers to a particular family of quantum error correcting codes, with the special property of being invariant under permutations of the qubits. Given integers g , n , and m , the two codewords are
where | D k m ⟩ {\displaystyle |D_{k}^{m}\rangle } are the Dicke states consisting of a uniform superposition of all weight-k words on m qubits, e.g.
The real parameter u = m g n {\displaystyle u={\frac {m}{gn}}} scales the density of the code. The length m = g n u {\displaystyle m=gnu} , hence the name of the code. For odd g = n {\displaystyle g=n} and u ≥ 1 {\displaystyle u\geq 1} , the gnu code is capable of correcting g − 1 2 {\displaystyle {\frac {g-1}{2}}} erasure errors, or deletion errors.