Devon Hjelm Notes/070827

Subsystem construction from 2 classical linear codes

First take 2 classical linear codes [math]\displaystyle{ C_1 }[/math] and [math]\displaystyle{ C_2 }[/math], which encode [math]\displaystyle{ k_1 }[/math] and [math]\displaystyle{ k_2 }[/math] bits into [math]\displaystyle{ n_1 }[/math] and [math]\displaystyle{ n_2 }[/math] bits respectively. Define a set of stabilizers [math]\displaystyle{ \mathcal{S}_1 }[/math] from [math]\displaystyle{ P_1 }[/math] as
[math]\displaystyle{ \mathcal{S}_1 = \langle S_1,S_2,\dots,S_{n-k} \rangle }[/math] with [math]\displaystyle{ S_i = Z }[/math]