Ex11 5

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 11.5}$

Show that if an $[[n,k,d]]$-quantum code is able to correct all errors of weight $t$ or less, $d \geq 2t +1$.