Gnu code

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" (the "gap"), "n" (the occupancy), and "m" (the length of the code), the two codewords are
where formula_3 are the Dicke states consisting of a uniform superposition of all weight-"k" words on "m" qubits, e.g.
The real parameter formula_5 scales the density of the code. The length formula_6, hence the name of the code. For odd formula_7 and formula_8, the gnu code is capable of correcting formula_9 erasure errors, or deletion errors.