In quantum error correction, CSS codes, named after their inventors, Robert Calderbank, Peter Shor and Andrew Steane, are a special type of Stabilizer codes constructed from classical codes with some special properties.
Let C 1 and C 2 be two (classical) [ n , k 1 ] , [ n , k 2 ] codes such, that C 2 ⊂ C 1 and C 1 , C 2 ⊥ both have minimal distance ≥ 2 t + 1 , where C 2 ⊥ is the code dual to C 2 . Then define CSS ( C 1 , C 2 ) , the CSS code of C 1 over C 2 as an [ n , k 1 − k 2 , d ] code, with d ≥ 2 t + 1 as follows:
Define for x ∈ C 1 : | x + C 2 ⟩ := 1 / | C 2 | ∑ y ∈ C 2 | x + y ⟩ , where + is bitwise addition modulo 2. Then CSS ( C 1 , C 2 ) is defined as { | x + C 2 ⟩ ∣ x ∈ C 1 } .
