Ex11 14

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.14}$

Show that $[[n,k]]$ quantum stabilizer code there is, for any $k$ bit string $b_1\dots b_k$, a unique element of the code $C$ that is a $(-1)^{b_i}$-eigenstate of $Z_i$ for all $i$.