I am studying the book "elements of information theory"- THOMAS M. COVER JOY A. THOMAS, and when it proves the channel coding theorem, one of the things it states is that all codes "C", are symmetric (refer to link). Could someone care to explain why this the codes construction is considered symmetric? All other previous proofs in the book make complete sense to me, it's just this affirmation that has me lost.
link (screenshot of the book where it states symmetry): https://gyazo.com/1cf69ee16a0c606a7c96044170a2945c
For reference, this is chapter 7 subsection 7 of the book previously mentioned.