An [ n , k ] {\displaystyle [n,k]} stabilizer code is defined to be the vector space V S {\displaystyle V_{S}} stabilized by a subgroup S {\displaystyle S} of G n {\displaystyle G_{n}} such that − I ∉ S {\displaystyle -I\notin S} and S {\displaystyle S} has n − k {\displaystyle n-k} independent and commuting generators, S = ⟨ g 1 , … , g n − k ⟩ {\displaystyle S=\langle g_{1},\ldots ,g_{n-k}\rangle } . Denote this code C ( S ) {\displaystyle C(S)} .
![{\displaystyle [n,k]}](/media/api/rest_v1/media/math/render/svg/4d9e3e5f03db243c10e64608605d156ae1885952)
