Ex11 12

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.12}$

Show that if two blocks encoded according to code $C$ are subjected to an error $E$ that is a superposition of errors $E = E_a\otimes E_b + E_c\otimes E_d$, where $E_a$, $E_b$, $E_c$, and $E_d$ are all elements of a correctable set of errors $\cal E$ for $C$, then $E$ can be corrected.