# 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.

## 1. error correction

- see Nielsen and Chuang
- a fact about parity is needed and is left as an exercise. yquek has a good proof for that exercise here