Английская Википедия:Gnu code

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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 (the gap), n (the occupancy), and m (the length of the code), the two codewords are

<math>|0_{\rm L}\rangle = \sum_{\ell\, \textrm{even}\atop 0\le\ell\le n} \sqrt{\fracШаблон:N\choose \ell{2^{n-1}}} |D^m_{g\ell}\rangle</math>

<math>|1_{\rm L}\rangle = \sum_{\ell\, \textrm{odd}\atop 0\le\ell\le n} \sqrt{\fracШаблон:N\choose \ell{2^{n-1}}} |D^m_{g\ell}\rangle</math>

where <math>|D^m_k\rangle</math> are the Dicke states consisting of a uniform superposition of all weight-k words on m qubits, e.g.

<math>|D^4_2\rangle = \frac{|0011\rangle + |0101\rangle + |1001\rangle + |0110\rangle + |1010\rangle + |1100\rangle}{\sqrt{6}}</math>

The real parameter <math>u = \frac{m}{gn}</math> scales the density of the code. The length <math>m = gnu</math>, hence the name of the code. For odd <math>g = n</math> and <math>u \ge 1</math>, the gnu code is capable of correcting <math>\frac{g-1}{2}</math> erasure errors, or deletion errors.