Quantum Codes Suitable for Iterative Decoding

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Definition of a stabilizer code
Quantum
◮ Let S be an Abelian subgroup of G n where all its elements are
of order 2 and such that −1 /∈ S. Such a subgroup is called an
admissible group.
◮ A stabilizer code C associated to an admissible group S is the
subspace of C 2n defined by
C = {|ψ〉 ∈ C 2n |∀M ∈ S, M|ψ〉 = |ψ〉}
S is called the stabilizer group of C. If S is generated by n − k
independent generators then dim C = 2 k .