# Stabilizer code

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An <math>[n,k]</math> **stabilizer code** is defined to be the vector space <math>V_S</math> stabilized by a subgroup <math>S</math> of <math>G_n</math> such that <math>-I\notin S</math> and <math>S</math> has <math>n-k</math> independent and commuting generators, <math>S=\langle g_1,\ldots,g_{n-k}\rangle</math>. These conditions are are required so that the vector space stabilized is non-trivial. Denote this code <math>C(S)</math>.

## References

- D. Gottesman, "Stabilizer codes and quantum error correction," quant-ph/9705052, Caltech Ph.D. thesis. http://arxiv.org/abs/quant-ph/9705052

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