css codes

• prerequisites \(C_2 \subset C_1\). such that \(C_1\) and \(C_2^\perp\) can each correct \(t\) errors.
• the codewords are

\[ \ket{x + C_2} = \frac{1}{\sqrt{|C_2|}}\sum_{y \in C_2} \ket{x+y} \] where \(x\) is some codeword in \(C_1\).

Here \(\ket{x+C_2}\) is a coset.